id	sid	tid	token	lemma	pos
ejpam-393	1	1	7_340_ahmed.dvi	7_340_ahmed.dvi	NUM
ejpam-393	1	2	european	european	ADJ
ejpam-393	1	3	journal	journal	PROPN
ejpam-393	1	4	of	of	ADP
ejpam-393	1	5	pure	pure	ADJ
ejpam-393	1	6	and	and	CCONJ
ejpam-393	1	7	applied	apply	VERB
ejpam-393	1	8	mathematics	mathematic	NOUN
ejpam-393	1	9	vol	vol	NOUN
ejpam-393	1	10	.	.	PUNCT
ejpam-393	2	1	3	3	NUM
ejpam-393	2	2	,	,	PUNCT
ejpam-393	2	3	no	no	INTJ
ejpam-393	2	4	.	.	NOUN
ejpam-393	2	5	5	5	NUM
ejpam-393	2	6	,	,	PUNCT
ejpam-393	2	7	2010	2010	NUM
ejpam-393	2	8	,	,	PUNCT
ejpam-393	2	9	853	853	NUM
ejpam-393	2	10	-	-	SYM
ejpam-393	2	11	880	880	NUM
ejpam-393	2	12	issn	issn	PROPN
ejpam-393	2	13	1307	1307	NUM
ejpam-393	2	14	-	-	SYM
ejpam-393	2	15	5543	5543	NUM
ejpam-393	2	16	–	–	PUNCT
ejpam-393	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-393	2	18	on	on	ADP
ejpam-393	2	19	neat	neat	ADJ
ejpam-393	2	20	reducts	reduct	NOUN
ejpam-393	2	21	of	of	ADP
ejpam-393	2	22	cylindric	cylindric	ADJ
ejpam-393	2	23	algebras	algebras	PROPN
ejpam-393	2	24	tarek	tarek	PROPN
ejpam-393	2	25	sayed	sayed	PROPN
ejpam-393	2	26	ahmed	ahmed	PROPN
ejpam-393	2	27	department	department	PROPN
ejpam-393	2	28	of	of	ADP
ejpam-393	2	29	mathematics	mathematic	NOUN
ejpam-393	2	30	,	,	PUNCT
ejpam-393	2	31	faculty	faculty	NOUN
ejpam-393	2	32	of	of	ADP
ejpam-393	2	33	science	science	NOUN
ejpam-393	2	34	,	,	PUNCT
ejpam-393	2	35	cairo	cairo	PROPN
ejpam-393	2	36	university	university	PROPN
ejpam-393	2	37	,	,	PUNCT
ejpam-393	2	38	giza	giza	PROPN
ejpam-393	2	39	,	,	PUNCT
ejpam-393	2	40	egypt	egypt	PROPN
ejpam-393	2	41	.	.	PUNCT
ejpam-393	3	1	abstract	abstract	PROPN
ejpam-393	3	2	.	.	PUNCT
ejpam-393	4	1	let	let	VERB
ejpam-393	4	2	1	1	NUM
ejpam-393	4	3	<	<	X
ejpam-393	4	4	n	n	X
ejpam-393	4	5	<	<	X
ejpam-393	4	6	m	m	NOUN
ejpam-393	4	7	≤ω	≤ω	ADJ
ejpam-393	4	8	.	.	PUNCT
ejpam-393	5	1	we	we	PRON
ejpam-393	5	2	investigate	investigate	VERB
ejpam-393	5	3	the	the	DET
ejpam-393	5	4	following	follow	VERB
ejpam-393	5	5	question	question	NOUN
ejpam-393	5	6	:	:	PUNCT
ejpam-393	5	7	for	for	ADP
ejpam-393	5	8	which	which	PRON
ejpam-393	5	9	reducts	reduct	NOUN
ejpam-393	5	10	of	of	ADP
ejpam-393	5	11	cam	cam	NOUN
ejpam-393	5	12	is	be	AUX
ejpam-393	5	13	the	the	DET
ejpam-393	5	14	class	class	NOUN
ejpam-393	5	15	of	of	ADP
ejpam-393	5	16	neat	neat	ADJ
ejpam-393	5	17	n	n	NOUN
ejpam-393	5	18	reducts	reduct	NOUN
ejpam-393	5	19	(	(	PUNCT
ejpam-393	5	20	not	not	PART
ejpam-393	5	21	)	)	PUNCT
ejpam-393	5	22	elementary	elementary	NOUN
ejpam-393	5	23	.	.	PUNCT
ejpam-393	6	1	we	we	PRON
ejpam-393	6	2	also	also	ADV
ejpam-393	6	3	characterize	characterize	VERB
ejpam-393	6	4	the	the	DET
ejpam-393	6	5	class	class	NOUN
ejpam-393	6	6	of	of	ADP
ejpam-393	6	7	neat	neat	ADJ
ejpam-393	6	8	reducts	reduct	NOUN
ejpam-393	6	9	using	use	VERB
ejpam-393	6	10	games	game	NOUN
ejpam-393	6	11	.	.	PUNCT
ejpam-393	7	1	2000	2000	NUM
ejpam-393	7	2	mathematics	mathematic	NOUN
ejpam-393	7	3	subject	subject	NOUN
ejpam-393	7	4	classifications	classification	NOUN
ejpam-393	7	5	:	:	PUNCT
ejpam-393	7	6	primary	primary	NOUN
ejpam-393	7	7	03g15	03g15	VERB
ejpam-393	7	8	,	,	PUNCT
ejpam-393	7	9	secondary	secondary	ADJ
ejpam-393	7	10	03c05	03c05	NUM
ejpam-393	7	11	,	,	PUNCT
ejpam-393	7	12	03c40	03c40	NUM
ejpam-393	7	13	key	key	ADJ
ejpam-393	7	14	words	word	NOUN
ejpam-393	7	15	and	and	CCONJ
ejpam-393	7	16	phrases	phrase	NOUN
ejpam-393	7	17	:	:	PUNCT
ejpam-393	7	18	algebraic	algebraic	ADJ
ejpam-393	7	19	logic	logic	NOUN
ejpam-393	7	20	,	,	PUNCT
ejpam-393	7	21	cylindric	cylindric	ADJ
ejpam-393	7	22	algebras	algebra	NOUN
ejpam-393	7	23	,	,	PUNCT
ejpam-393	7	24	neat	neat	ADJ
ejpam-393	7	25	reducts	reduct	NOUN
ejpam-393	7	26	1	1	NUM
ejpam-393	7	27	.	.	PUNCT
ejpam-393	8	1	the	the	DET
ejpam-393	8	2	class	class	NOUN
ejpam-393	8	3	of	of	ADP
ejpam-393	8	4	neat	neat	ADJ
ejpam-393	8	5	reducts	reduct	NOUN
ejpam-393	8	6	neat	neat	ADJ
ejpam-393	8	7	reducts	reduct	NOUN
ejpam-393	8	8	have	have	AUX
ejpam-393	8	9	been	be	AUX
ejpam-393	8	10	a	a	DET
ejpam-393	8	11	central	central	ADJ
ejpam-393	8	12	notion	notion	NOUN
ejpam-393	8	13	in	in	ADP
ejpam-393	8	14	algebraic	algebraic	ADJ
ejpam-393	8	15	logic	logic	NOUN
ejpam-393	8	16	since	since	SCONJ
ejpam-393	8	17	the	the	DET
ejpam-393	8	18	very	very	ADJ
ejpam-393	8	19	beginning	beginning	NOUN
ejpam-393	8	20	,	,	PUNCT
ejpam-393	8	21	and	and	CCONJ
ejpam-393	8	22	the	the	DET
ejpam-393	8	23	notion	notion	NOUN
ejpam-393	8	24	is	be	AUX
ejpam-393	8	25	still	still	ADV
ejpam-393	8	26	a	a	DET
ejpam-393	8	27	versatile	versatile	ADV
ejpam-393	8	28	active	active	ADJ
ejpam-393	8	29	field	field	NOUN
ejpam-393	8	30	of	of	ADP
ejpam-393	8	31	research	research	NOUN
ejpam-393	8	32	,	,	PUNCT
ejpam-393	9	1	[	[	X
ejpam-393	9	2	see	see	VERB
ejpam-393	9	3	e.g	e.g	PROPN
ejpam-393	9	4	18	18	NUM
ejpam-393	9	5	,	,	PUNCT
ejpam-393	9	6	21	21	NUM
ejpam-393	9	7	,	,	PUNCT
ejpam-393	9	8	34	34	NUM
ejpam-393	9	9	,	,	PUNCT
ejpam-393	9	10	31	31	NUM
ejpam-393	9	11	,	,	PUNCT
ejpam-393	9	12	43	43	NUM
ejpam-393	9	13	,	,	PUNCT
ejpam-393	9	14	24	24	NUM
ejpam-393	9	15	,	,	PUNCT
ejpam-393	9	16	45	45	NUM
ejpam-393	9	17	,	,	PUNCT
ejpam-393	9	18	41	41	NUM
ejpam-393	9	19	,	,	PUNCT
ejpam-393	9	20	42	42	NUM
ejpam-393	9	21	,	,	PUNCT
ejpam-393	9	22	30	30	NUM
ejpam-393	9	23	,	,	PUNCT
ejpam-393	9	24	33	33	NUM
ejpam-393	9	25	]	]	PUNCT
ejpam-393	9	26	.	.	PUNCT
ejpam-393	10	1	indeed	indeed	ADV
ejpam-393	10	2	,	,	PUNCT
ejpam-393	10	3	the	the	DET
ejpam-393	10	4	consecutive	consecutive	ADJ
ejpam-393	10	5	problems	problem	NOUN
ejpam-393	10	6	2.11	2.11	NUM
ejpam-393	10	7	,	,	PUNCT
ejpam-393	10	8	2.12	2.12	NUM
ejpam-393	10	9	,	,	PUNCT
ejpam-393	10	10	2.13	2.13	NUM
ejpam-393	10	11	in	in	ADP
ejpam-393	10	12	the	the	DET
ejpam-393	10	13	monograph	monograph	NOUN
ejpam-393	11	1	[	[	X
ejpam-393	11	2	11	11	NUM
ejpam-393	11	3	]	]	PUNCT
ejpam-393	11	4	are	be	AUX
ejpam-393	11	5	on	on	ADP
ejpam-393	11	6	neat	neat	ADJ
ejpam-393	11	7	reducts	reduct	NOUN
ejpam-393	11	8	.	.	PUNCT
ejpam-393	12	1	problem	problem	NOUN
ejpam-393	12	2	2.12	2.12	NUM
ejpam-393	12	3	is	be	AUX
ejpam-393	12	4	solved	solve	VERB
ejpam-393	12	5	by	by	ADP
ejpam-393	12	6	hirsch	hirsch	PROPN
ejpam-393	12	7	hodkinson	hodkinson	PROPN
ejpam-393	12	8	and	and	CCONJ
ejpam-393	12	9	maddux	maddux	PROPN
ejpam-393	13	1	[	[	X
ejpam-393	13	2	10	10	NUM
ejpam-393	13	3	]	]	PUNCT
ejpam-393	13	4	.	.	PUNCT
ejpam-393	14	1	the	the	DET
ejpam-393	14	2	authors	author	NOUN
ejpam-393	14	3	of	of	ADP
ejpam-393	14	4	[	[	X
ejpam-393	14	5	10	10	NUM
ejpam-393	14	6	]	]	PUNCT
ejpam-393	14	7	show	show	VERB
ejpam-393	14	8	that	that	SCONJ
ejpam-393	14	9	the	the	DET
ejpam-393	14	10	sequence	sequence	NOUN
ejpam-393	14	11	〈	〈	NOUN
ejpam-393	14	12	snrncan+k	snrncan+k	PROPN
ejpam-393	14	13	:	:	PUNCT
ejpam-393	14	14	k	k	PROPN
ejpam-393	14	15	∈	∈	PROPN
ejpam-393	14	16	ω	ω	NUM
ejpam-393	14	17	〉	〉	NOUN
ejpam-393	14	18	is	be	AUX
ejpam-393	14	19	strictly	strictly	ADV
ejpam-393	14	20	decreasing	decrease	VERB
ejpam-393	14	21	for	for	ADP
ejpam-393	14	22	ω	ω	PROPN
ejpam-393	14	23	>	>	X
ejpam-393	14	24	n	n	PROPN
ejpam-393	14	25	>	>	X
ejpam-393	14	26	2	2	NUM
ejpam-393	14	27	with	with	ADP
ejpam-393	14	28	respect	respect	NOUN
ejpam-393	14	29	to	to	ADP
ejpam-393	14	30	inclusion	inclusion	NOUN
ejpam-393	14	31	.	.	PUNCT
ejpam-393	15	1	(	(	PUNCT
ejpam-393	15	2	recall	recall	VERB
ejpam-393	15	3	that	that	SCONJ
ejpam-393	15	4	we	we	PRON
ejpam-393	15	5	generalized	generalize	VERB
ejpam-393	15	6	this	this	DET
ejpam-393	15	7	result	result	NOUN
ejpam-393	15	8	to	to	ADP
ejpam-393	15	9	quasipolyadic	quasipolyadic	ADJ
ejpam-393	15	10	equality	equality	NOUN
ejpam-393	15	11	algebras	algebra	NOUN
ejpam-393	15	12	)	)	PUNCT
ejpam-393	15	13	.	.	PUNCT
ejpam-393	16	1	the	the	DET
ejpam-393	16	2	infinite	infinite	ADJ
ejpam-393	16	3	dimensional	dimensional	ADJ
ejpam-393	16	4	case	case	NOUN
ejpam-393	16	5	is	be	AUX
ejpam-393	16	6	settled	settle	VERB
ejpam-393	16	7	by	by	ADP
ejpam-393	16	8	pigozzi	pigozzi	NOUN
ejpam-393	16	9	as	as	SCONJ
ejpam-393	16	10	reported	report	VERB
ejpam-393	16	11	in	in	ADP
ejpam-393	16	12	[	[	X
ejpam-393	16	13	11	11	NUM
ejpam-393	16	14	]	]	PUNCT
ejpam-393	16	15	.	.	PUNCT
ejpam-393	17	1	the	the	DET
ejpam-393	17	2	main	main	ADJ
ejpam-393	17	3	result	result	NOUN
ejpam-393	17	4	in	in	ADP
ejpam-393	17	5	[	[	X
ejpam-393	17	6	10	10	NUM
ejpam-393	17	7	]	]	PUNCT
ejpam-393	17	8	strengthes	strengthe	VERB
ejpam-393	17	9	monk	monk	NOUN
ejpam-393	17	10	’s	’s	PART
ejpam-393	17	11	classical	classical	ADJ
ejpam-393	17	12	result	result	NOUN
ejpam-393	17	13	that	that	SCONJ
ejpam-393	17	14	for	for	ADP
ejpam-393	17	15	every	every	DET
ejpam-393	17	16	finite	finite	NOUN
ejpam-393	17	17	n	n	CCONJ
ejpam-393	17	18	>	>	SYM
ejpam-393	17	19	2	2	NUM
ejpam-393	17	20	and	and	CCONJ
ejpam-393	17	21	any	any	DET
ejpam-393	17	22	k	k	PROPN
ejpam-393	17	23	∈	∈	PROPN
ejpam-393	17	24	ω	ω	PROPN
ejpam-393	17	25	,	,	PUNCT
ejpam-393	17	26	rcan	rcan	PROPN
ejpam-393	17	27	⊂	⊂	PROPN
ejpam-393	17	28	snrncan+k	snrncan+k	PROPN
ejpam-393	17	29	.	.	PUNCT
ejpam-393	18	1	taking	take	VERB
ejpam-393	18	2	ak	ak	PROPN
ejpam-393	18	3	∈	∈	PROPN
ejpam-393	18	4	snrncan+k	snrncan+k	PROPN
ejpam-393	18	5	∼	∼	NOUN
ejpam-393	18	6	rcan	rcan	NOUN
ejpam-393	18	7	,	,	PUNCT
ejpam-393	18	8	and	and	CCONJ
ejpam-393	18	9	forming	form	VERB
ejpam-393	18	10	the	the	DET
ejpam-393	18	11	ultraproduct	ultraproduct	ADJ
ejpam-393	18	12	∏	∏	PROPN
ejpam-393	18	13	ak	ak	PROPN
ejpam-393	18	14	/	/	SYM
ejpam-393	18	15	f	f	PROPN
ejpam-393	18	16	relative	relative	ADJ
ejpam-393	18	17	to	to	ADP
ejpam-393	18	18	a	a	DET
ejpam-393	18	19	non	non	ADJ
ejpam-393	18	20	-	-	ADJ
ejpam-393	18	21	principal	principal	ADJ
ejpam-393	18	22	ultrafilter	ultrafilter	NOUN
ejpam-393	18	23	on	on	ADP
ejpam-393	18	24	ω	ω	NUM
ejpam-393	18	25	,	,	PUNCT
ejpam-393	18	26	the	the	DET
ejpam-393	18	27	resulting	result	VERB
ejpam-393	18	28	structure	structure	NOUN
ejpam-393	18	29	will	will	AUX
ejpam-393	18	30	be	be	AUX
ejpam-393	18	31	representable	representable	ADJ
ejpam-393	18	32	,	,	PUNCT
ejpam-393	18	33	showing	show	VERB
ejpam-393	18	34	that	that	DET
ejpam-393	18	35	rcan	rcan	NOUN
ejpam-393	18	36	,	,	PUNCT
ejpam-393	18	37	though	though	ADV
ejpam-393	18	38	,	,	PUNCT
ejpam-393	18	39	elementary	elementary	NOUN
ejpam-393	18	40	(	(	PUNCT
ejpam-393	18	41	indeed	indeed	ADV
ejpam-393	18	42	a	a	DET
ejpam-393	18	43	variety	variety	NOUN
ejpam-393	18	44	)	)	PUNCT
ejpam-393	18	45	is	be	AUX
ejpam-393	18	46	not	not	PART
ejpam-393	18	47	finitely	finitely	ADV
ejpam-393	18	48	axiomatizable	axiomatizable	ADJ
ejpam-393	18	49	.	.	PUNCT
ejpam-393	19	1	problem	problem	NOUN
ejpam-393	19	2	2.13	2.13	NUM
ejpam-393	19	3	is	be	AUX
ejpam-393	19	4	solved	solve	VERB
ejpam-393	19	5	in	in	ADP
ejpam-393	19	6	[	[	X
ejpam-393	19	7	41	41	NUM
ejpam-393	19	8	]	]	PUNCT
ejpam-393	19	9	.	.	PUNCT
ejpam-393	20	1	problem	problem	NOUN
ejpam-393	20	2	2.11	2.11	NUM
ejpam-393	20	3	which	which	PRON
ejpam-393	20	4	is	be	AUX
ejpam-393	20	5	relevant	relevant	ADJ
ejpam-393	20	6	to	to	ADP
ejpam-393	20	7	our	our	PRON
ejpam-393	20	8	later	later	ADJ
ejpam-393	20	9	discussion	discussion	NOUN
ejpam-393	20	10	asks	ask	VERB
ejpam-393	20	11	:	:	PUNCT
ejpam-393	20	12	for	for	SCONJ
ejpam-393	20	13	which	which	DET
ejpam-393	20	14	pair	pair	NOUN
ejpam-393	20	15	of	of	ADP
ejpam-393	20	16	ordinals	ordinal	NOUN
ejpam-393	20	17	α	α	PROPN
ejpam-393	20	18	<	<	X
ejpam-393	20	19	β	β	X
ejpam-393	20	20	is	be	AUX
ejpam-393	20	21	the	the	DET
ejpam-393	20	22	class	class	NOUN
ejpam-393	20	23	nrαcaβ	nrαcaβ	NOUN
ejpam-393	20	24	closed	close	VERB
ejpam-393	20	25	under	under	ADP
ejpam-393	20	26	forming	form	VERB
ejpam-393	20	27	subalgebras	subalgebra	NOUN
ejpam-393	20	28	and	and	CCONJ
ejpam-393	20	29	homomorphic	homomorphic	ADJ
ejpam-393	20	30	images	image	NOUN
ejpam-393	20	31	?	?	PUNCT
ejpam-393	21	1	németi	németi	PROPN
ejpam-393	21	2	proves	prove	VERB
ejpam-393	21	3	that	that	SCONJ
ejpam-393	21	4	for	for	ADP
ejpam-393	21	5	any	any	DET
ejpam-393	21	6	1	1	NUM
ejpam-393	21	7	<	<	X
ejpam-393	21	8	α	α	X
ejpam-393	21	9	<	<	X
ejpam-393	21	10	β	β	X
ejpam-393	21	11	the	the	DET
ejpam-393	21	12	class	class	NOUN
ejpam-393	21	13	nrαcaβ	nrαcaβ	ADJ
ejpam-393	21	14	though	though	ADV
ejpam-393	21	15	closed	close	VERB
ejpam-393	21	16	under	under	ADP
ejpam-393	21	17	forming	form	VERB
ejpam-393	21	18	homomorphic	homomorphic	ADJ
ejpam-393	21	19	images	image	NOUN
ejpam-393	21	20	and	and	CCONJ
ejpam-393	21	21	products	product	NOUN
ejpam-393	21	22	is	be	AUX
ejpam-393	21	23	not	not	PART
ejpam-393	21	24	a	a	DET
ejpam-393	21	25	variety	variety	NOUN
ejpam-393	21	26	,	,	PUNCT
ejpam-393	21	27	i.e.	i.e.	X
ejpam-393	21	28	,	,	PUNCT
ejpam-393	21	29	it	it	PRON
ejpam-393	21	30	is	be	AUX
ejpam-393	21	31	not	not	PART
ejpam-393	21	32	closed	close	VERB
ejpam-393	21	33	under	under	ADP
ejpam-393	21	34	forming	form	VERB
ejpam-393	21	35	subalgebras	subalgebra	NOUN
ejpam-393	22	1	[	[	X
ejpam-393	22	2	14	14	NUM
ejpam-393	22	3	]	]	PUNCT
ejpam-393	22	4	.	.	PUNCT
ejpam-393	23	1	the	the	DET
ejpam-393	23	2	next	next	ADJ
ejpam-393	23	3	natural	natural	ADJ
ejpam-393	23	4	question	question	NOUN
ejpam-393	23	5	is	be	AUX
ejpam-393	23	6	whether	whether	SCONJ
ejpam-393	23	7	this	this	DET
ejpam-393	23	8	class	class	NOUN
ejpam-393	23	9	is	be	AUX
ejpam-393	23	10	elementary	elementary	ADJ
ejpam-393	23	11	,	,	PUNCT
ejpam-393	23	12	and	and	CCONJ
ejpam-393	23	13	in	in	ADP
ejpam-393	23	14	this	this	DET
ejpam-393	23	15	particular	particular	ADJ
ejpam-393	23	16	case	case	NOUN
ejpam-393	23	17	,	,	PUNCT
ejpam-393	23	18	since	since	SCONJ
ejpam-393	23	19	the	the	DET
ejpam-393	23	20	class	class	NOUN
ejpam-393	23	21	of	of	ADP
ejpam-393	23	22	neat	neat	ADJ
ejpam-393	23	23	reducts	reduct	NOUN
ejpam-393	23	24	is	be	AUX
ejpam-393	23	25	closed	close	VERB
ejpam-393	23	26	under	under	ADP
ejpam-393	23	27	ultraproducts	ultraproduct	NOUN
ejpam-393	23	28	,	,	PUNCT
ejpam-393	23	29	this	this	PRON
ejpam-393	23	30	amounts	amount	VERB
ejpam-393	23	31	to	to	ADP
ejpam-393	23	32	asking	ask	VERB
ejpam-393	23	33	whether	whether	SCONJ
ejpam-393	23	34	it	it	PRON
ejpam-393	23	35	is	be	AUX
ejpam-393	23	36	closed	close	VERB
ejpam-393	23	37	under	under	ADP
ejpam-393	23	38	elementary	elementary	ADJ
ejpam-393	23	39	subalgebras	subalgebras	PROPN
ejpam-393	23	40	?	?	PUNCT
ejpam-393	24	1	in	in	ADP
ejpam-393	24	2	[	[	X
ejpam-393	24	3	18	18	NUM
ejpam-393	24	4	]	]	X
ejpam-393	24	5	it	it	PRON
ejpam-393	24	6	is	be	AUX
ejpam-393	24	7	proved	prove	VERB
ejpam-393	24	8	that	that	SCONJ
ejpam-393	24	9	for	for	ADP
ejpam-393	24	10	any	any	DET
ejpam-393	24	11	1	1	NUM
ejpam-393	24	12	<	<	X
ejpam-393	24	13	α	α	X
ejpam-393	24	14	<	<	X
ejpam-393	24	15	β	β	X
ejpam-393	24	16	,	,	PUNCT
ejpam-393	24	17	the	the	DET
ejpam-393	24	18	class	class	NOUN
ejpam-393	24	19	nrαcaβ	nrαcaβ	NOUN
ejpam-393	24	20	is	be	AUX
ejpam-393	24	21	not	not	PART
ejpam-393	24	22	elementary	elementary	ADJ
ejpam-393	24	23	answering	answering	NOUN
ejpam-393	24	24	problem	problem	NOUN
ejpam-393	24	25	4.4	4.4	NUM
ejpam-393	24	26	in	in	ADP
ejpam-393	24	27	[	[	X
ejpam-393	24	28	12	12	NUM
ejpam-393	24	29	]	]	PUNCT
ejpam-393	24	30	.	.	PUNCT
ejpam-393	25	1	in	in	ADP
ejpam-393	25	2	[	[	X
ejpam-393	25	3	30	30	NUM
ejpam-393	25	4	]	]	PUNCT
ejpam-393	25	5	,	,	PUNCT
ejpam-393	25	6	it	it	PRON
ejpam-393	25	7	is	be	AUX
ejpam-393	25	8	shown	show	VERB
ejpam-393	25	9	that	that	SCONJ
ejpam-393	25	10	this	this	DET
ejpam-393	25	11	class	class	NOUN
ejpam-393	25	12	can	can	AUX
ejpam-393	25	13	not	not	PART
ejpam-393	25	14	be	be	AUX
ejpam-393	25	15	characterized	characterize	VERB
ejpam-393	25	16	by	by	ADP
ejpam-393	25	17	any	any	DET
ejpam-393	25	18	l∞ω	l∞ω	ADJ
ejpam-393	25	19	sentence	sentence	NOUN
ejpam-393	25	20	.	.	PUNCT
ejpam-393	26	1	we	we	PRON
ejpam-393	26	2	know	know	VERB
ejpam-393	26	3	that	that	SCONJ
ejpam-393	26	4	nrncaω	nrncaω	ADJ
ejpam-393	26	5	email	email	NOUN
ejpam-393	26	6	address	address	NOUN
ejpam-393	26	7	:	:	PUNCT
ejpam-393	26	8	rutahmed	rutahme	VERB
ejpam-393	26	9	�	�	NOUN
ejpam-393	26	10	gmail	gmail	NOUN
ejpam-393	26	11	.	.	PUNCT
ejpam-393	27	1	om	om	PROPN
ejpam-393	27	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-393	27	3	853	853	NUM
ejpam-393	28	1	c	c	NOUN
ejpam-393	28	2	©	©	PROPN
ejpam-393	28	3	2010	2010	NUM
ejpam-393	28	4	ejpam	ejpam	NOUN
ejpam-393	28	5	all	all	DET
ejpam-393	28	6	rights	right	NOUN
ejpam-393	28	7	reserved	reserve	VERB
ejpam-393	28	8	.	.	PUNCT
ejpam-393	29	1	t.	t.	PROPN
ejpam-393	29	2	ahmed	ahmed	PROPN
ejpam-393	29	3	/	/	SYM
ejpam-393	29	4	eur	eur	PROPN
ejpam-393	29	5	.	.	PUNCT
ejpam-393	30	1	j.	j.	PROPN
ejpam-393	30	2	pure	pure	PROPN
ejpam-393	30	3	appl	appl	PROPN
ejpam-393	30	4	.	.	PROPN
ejpam-393	30	5	math	math	PROPN
ejpam-393	30	6	,	,	PUNCT
ejpam-393	30	7	3	3	NUM
ejpam-393	30	8	(	(	PUNCT
ejpam-393	30	9	2010	2010	NUM
ejpam-393	30	10	)	)	PUNCT
ejpam-393	30	11	,	,	PUNCT
ejpam-393	30	12	853	853	NUM
ejpam-393	30	13	-	-	SYM
ejpam-393	30	14	880	880	NUM
ejpam-393	30	15	854	854	NUM
ejpam-393	30	16	is	be	AUX
ejpam-393	30	17	closed	close	VERB
ejpam-393	30	18	under	under	ADP
ejpam-393	30	19	products	product	NOUN
ejpam-393	30	20	and	and	CCONJ
ejpam-393	30	21	homomorphic	homomorphic	ADJ
ejpam-393	30	22	images	image	NOUN
ejpam-393	30	23	,	,	PUNCT
ejpam-393	30	24	thus	thus	ADV
ejpam-393	30	25	under	under	ADP
ejpam-393	30	26	ultraproducts	ultraproduct	NOUN
ejpam-393	30	27	.	.	PUNCT
ejpam-393	31	1	however	however	ADV
ejpam-393	31	2	,	,	PUNCT
ejpam-393	31	3	for	for	ADP
ejpam-393	31	4	n	n	PROPN
ejpam-393	31	5	>	>	X
ejpam-393	31	6	1	1	NUM
ejpam-393	31	7	,	,	PUNCT
ejpam-393	31	8	it	it	PRON
ejpam-393	31	9	is	be	AUX
ejpam-393	31	10	not	not	PART
ejpam-393	31	11	closed	close	VERB
ejpam-393	31	12	under	under	ADP
ejpam-393	31	13	elementary	elementary	ADJ
ejpam-393	31	14	subalgebras	subalgebras	PROPN
ejpam-393	31	15	,	,	PUNCT
ejpam-393	31	16	equivalently	equivalently	ADV
ejpam-393	31	17	,	,	PUNCT
ejpam-393	31	18	under	under	ADP
ejpam-393	31	19	ultraroots	ultraroot	NOUN
ejpam-393	31	20	.	.	PUNCT
ejpam-393	32	1	(	(	PUNCT
ejpam-393	32	2	for	for	ADP
ejpam-393	32	3	n	n	PRON
ejpam-393	32	4	≤	≤	NOUN
ejpam-393	32	5	1,nrncaω	1,nrncaω	NUM
ejpam-393	32	6	=	=	SYM
ejpam-393	32	7	rcan	rcan	NOUN
ejpam-393	32	8	=	=	PUNCT
ejpam-393	32	9	can	can	AUX
ejpam-393	32	10	;	;	PUNCT
ejpam-393	32	11	so	so	CCONJ
ejpam-393	32	12	this	this	PRON
ejpam-393	32	13	is	be	AUX
ejpam-393	32	14	a	a	DET
ejpam-393	32	15	degenerate	degenerate	ADJ
ejpam-393	32	16	case	case	NOUN
ejpam-393	32	17	which	which	PRON
ejpam-393	32	18	we	we	PRON
ejpam-393	32	19	ignore	ignore	VERB
ejpam-393	32	20	)	)	PUNCT
ejpam-393	32	21	.	.	PUNCT
ejpam-393	33	1	for	for	ADP
ejpam-393	33	2	a	a	DET
ejpam-393	33	3	class	class	NOUN
ejpam-393	33	4	k	k	PROPN
ejpam-393	33	5	,	,	PUNCT
ejpam-393	33	6	e	e	PROPN
ejpam-393	33	7	lk	lk	PROPN
ejpam-393	33	8	denotes	denote	VERB
ejpam-393	33	9	the	the	DET
ejpam-393	33	10	elementary	elementary	ADJ
ejpam-393	33	11	closure	closure	NOUN
ejpam-393	33	12	of	of	ADP
ejpam-393	33	13	k	k	PROPN
ejpam-393	33	14	,	,	PUNCT
ejpam-393	33	15	that	that	PRON
ejpam-393	33	16	is	be	AUX
ejpam-393	33	17	the	the	DET
ejpam-393	33	18	least	least	ADJ
ejpam-393	33	19	elementary	elementary	ADJ
ejpam-393	33	20	class	class	NOUN
ejpam-393	33	21	containing	contain	VERB
ejpam-393	33	22	k	k	PROPN
ejpam-393	33	23	.	.	PUNCT
ejpam-393	34	1	upk	upk	PROPN
ejpam-393	34	2	denotes	denote	VERB
ejpam-393	34	3	the	the	DET
ejpam-393	34	4	class	class	NOUN
ejpam-393	34	5	of	of	ADP
ejpam-393	34	6	all	all	DET
ejpam-393	34	7	ultraproducts	ultraproduct	NOUN
ejpam-393	34	8	of	of	ADP
ejpam-393	34	9	members	member	NOUN
ejpam-393	34	10	of	of	ADP
ejpam-393	34	11	k	k	PROPN
ejpam-393	34	12	and	and	CCONJ
ejpam-393	34	13	urk	urk	PROPN
ejpam-393	34	14	denotes	denote	VERB
ejpam-393	34	15	the	the	DET
ejpam-393	34	16	class	class	NOUN
ejpam-393	34	17	of	of	ADP
ejpam-393	34	18	all	all	DET
ejpam-393	34	19	ultraroots	ultraroot	NOUN
ejpam-393	34	20	of	of	ADP
ejpam-393	34	21	members	member	NOUN
ejpam-393	34	22	of	of	ADP
ejpam-393	34	23	k	k	PROPN
ejpam-393	34	24	.	.	PUNCT
ejpam-393	35	1	recall	recall	VERB
ejpam-393	35	2	that	that	PRON
ejpam-393	35	3	,	,	PUNCT
ejpam-393	35	4	by	by	ADP
ejpam-393	35	5	the	the	DET
ejpam-393	35	6	celebrated	celebrate	VERB
ejpam-393	35	7	shelah	shelah	PROPN
ejpam-393	35	8	keisler	keisler	PROPN
ejpam-393	35	9	theorem	theorem	PROPN
ejpam-393	35	10	,	,	PUNCT
ejpam-393	35	11	elk	elk	NOUN
ejpam-393	35	12	=	=	SYM
ejpam-393	35	13	upurk	upurk	X
ejpam-393	35	14	.	.	PUNCT
ejpam-393	36	1	theorem	theorem	ADJ
ejpam-393	36	2	1	1	NUM
ejpam-393	36	3	.	.	PUNCT
ejpam-393	37	1	let	let	VERB
ejpam-393	37	2	n	n	PRON
ejpam-393	37	3	>	>	X
ejpam-393	37	4	1	1	X
ejpam-393	37	5	.	.	PUNCT
ejpam-393	38	1	then	then	ADV
ejpam-393	38	2	the	the	DET
ejpam-393	38	3	class	class	NOUN
ejpam-393	38	4	nrncaω	nrncaω	PROPN
ejpam-393	38	5	is	be	AUX
ejpam-393	38	6	pseudo	pseudo	NOUN
ejpam-393	38	7	-	-	NOUN
ejpam-393	38	8	elementary	elementary	ADJ
ejpam-393	38	9	,	,	PUNCT
ejpam-393	38	10	but	but	CCONJ
ejpam-393	38	11	is	be	AUX
ejpam-393	38	12	not	not	PART
ejpam-393	38	13	elementary	elementary	ADJ
ejpam-393	38	14	.	.	PUNCT
ejpam-393	39	1	furthermore	furthermore	ADV
ejpam-393	39	2	,	,	PUNCT
ejpam-393	39	3	elnrncaω	elnrncaω	PROPN
ejpam-393	39	4	⊂	⊂	PROPN
ejpam-393	39	5	rcan	rcan	PROPN
ejpam-393	39	6	,	,	PUNCT
ejpam-393	39	7	e	e	X
ejpam-393	39	8	lnrncaω	lnrncaω	PROPN
ejpam-393	39	9	is	be	AUX
ejpam-393	39	10	recursively	recursively	ADV
ejpam-393	39	11	enumerable	enumerable	ADJ
ejpam-393	39	12	,	,	PUNCT
ejpam-393	39	13	and	and	CCONJ
ejpam-393	39	14	for	for	ADP
ejpam-393	39	15	n	n	NOUN
ejpam-393	39	16	>	>	X
ejpam-393	39	17	2	2	NUM
ejpam-393	39	18	is	be	AUX
ejpam-393	39	19	not	not	PART
ejpam-393	39	20	finitely	finitely	ADV
ejpam-393	39	21	axiomatizable	axiomatizable	ADJ
ejpam-393	39	22	.	.	PUNCT
ejpam-393	40	1	proof	proof	NOUN
ejpam-393	40	2	.	.	PUNCT
ejpam-393	41	1	the	the	DET
ejpam-393	41	2	class	class	NOUN
ejpam-393	41	3	nrncaω	nrncaω	PROPN
ejpam-393	41	4	is	be	AUX
ejpam-393	41	5	not	not	PART
ejpam-393	41	6	elementary	elementary	ADJ
ejpam-393	41	7	[	[	X
ejpam-393	41	8	18	18	NUM
ejpam-393	41	9	]	]	PUNCT
ejpam-393	41	10	.	.	PUNCT
ejpam-393	42	1	to	to	PART
ejpam-393	42	2	show	show	VERB
ejpam-393	42	3	that	that	SCONJ
ejpam-393	42	4	it	it	PRON
ejpam-393	42	5	is	be	AUX
ejpam-393	42	6	pseudo	pseudo	NOUN
ejpam-393	42	7	-	-	NOUN
ejpam-393	42	8	elementary	elementary	ADJ
ejpam-393	42	9	,	,	PUNCT
ejpam-393	42	10	we	we	PRON
ejpam-393	42	11	use	use	VERB
ejpam-393	42	12	a	a	DET
ejpam-393	42	13	three	three	NUM
ejpam-393	42	14	sorted	sorted	ADJ
ejpam-393	42	15	defining	define	VERB
ejpam-393	42	16	theory	theory	NOUN
ejpam-393	42	17	,	,	PUNCT
ejpam-393	42	18	with	with	ADP
ejpam-393	42	19	one	one	NUM
ejpam-393	42	20	sort	sort	NOUN
ejpam-393	42	21	for	for	ADP
ejpam-393	42	22	a	a	DET
ejpam-393	42	23	cylindric	cylindric	ADJ
ejpam-393	42	24	algebra	algebra	NOUN
ejpam-393	42	25	of	of	ADP
ejpam-393	42	26	dimension	dimension	NOUN
ejpam-393	42	27	n(c	n(c	PROPN
ejpam-393	42	28	)	)	PUNCT
ejpam-393	42	29	,	,	PUNCT
ejpam-393	42	30	the	the	DET
ejpam-393	42	31	second	second	ADJ
ejpam-393	42	32	sort	sort	NOUN
ejpam-393	42	33	for	for	ADP
ejpam-393	42	34	the	the	DET
ejpam-393	42	35	boolean	boolean	ADJ
ejpam-393	42	36	reduct	reduct	NOUN
ejpam-393	42	37	of	of	ADP
ejpam-393	42	38	a	a	DET
ejpam-393	42	39	cylindric	cylindric	ADJ
ejpam-393	42	40	algebra	algebra	NOUN
ejpam-393	42	41	(	(	PUNCT
ejpam-393	42	42	b	b	NOUN
ejpam-393	42	43	)	)	PUNCT
ejpam-393	42	44	and	and	CCONJ
ejpam-393	42	45	the	the	DET
ejpam-393	42	46	third	third	ADJ
ejpam-393	42	47	sort	sort	NOUN
ejpam-393	42	48	for	for	ADP
ejpam-393	42	49	a	a	DET
ejpam-393	42	50	set	set	NOUN
ejpam-393	42	51	of	of	ADP
ejpam-393	42	52	dimensions	dimension	NOUN
ejpam-393	42	53	(	(	PUNCT
ejpam-393	42	54	δ	δ	PROPN
ejpam-393	42	55	)	)	PUNCT
ejpam-393	42	56	.	.	PUNCT
ejpam-393	43	1	we	we	PRON
ejpam-393	43	2	use	use	VERB
ejpam-393	43	3	superscripts	superscript	NOUN
ejpam-393	43	4	n	n	CCONJ
ejpam-393	43	5	,	,	PUNCT
ejpam-393	43	6	b	b	PROPN
ejpam-393	43	7	,	,	PUNCT
ejpam-393	43	8	δ	δ	PROPN
ejpam-393	43	9	for	for	ADP
ejpam-393	43	10	variables	variable	NOUN
ejpam-393	43	11	and	and	CCONJ
ejpam-393	43	12	functions	function	NOUN
ejpam-393	43	13	to	to	PART
ejpam-393	43	14	indicate	indicate	VERB
ejpam-393	43	15	that	that	SCONJ
ejpam-393	43	16	the	the	DET
ejpam-393	43	17	variable	variable	NOUN
ejpam-393	43	18	,	,	PUNCT
ejpam-393	43	19	or	or	CCONJ
ejpam-393	43	20	the	the	DET
ejpam-393	43	21	returned	return	VERB
ejpam-393	43	22	value	value	NOUN
ejpam-393	43	23	of	of	ADP
ejpam-393	43	24	the	the	DET
ejpam-393	43	25	function	function	NOUN
ejpam-393	43	26	,	,	PUNCT
ejpam-393	43	27	is	be	AUX
ejpam-393	43	28	of	of	ADP
ejpam-393	43	29	the	the	DET
ejpam-393	43	30	sort	sort	NOUN
ejpam-393	43	31	of	of	ADP
ejpam-393	43	32	the	the	DET
ejpam-393	43	33	cylindric	cylindric	ADJ
ejpam-393	43	34	algebra	algebra	NOUN
ejpam-393	43	35	of	of	ADP
ejpam-393	43	36	dimension	dimension	NOUN
ejpam-393	43	37	n	n	CCONJ
ejpam-393	43	38	,	,	PUNCT
ejpam-393	43	39	the	the	DET
ejpam-393	43	40	boolean	boolean	ADJ
ejpam-393	43	41	part	part	NOUN
ejpam-393	43	42	of	of	ADP
ejpam-393	43	43	the	the	DET
ejpam-393	43	44	cylindric	cylindric	ADJ
ejpam-393	43	45	algebra	algebra	NOUN
ejpam-393	43	46	or	or	CCONJ
ejpam-393	43	47	the	the	DET
ejpam-393	43	48	dimension	dimension	NOUN
ejpam-393	43	49	set	set	NOUN
ejpam-393	43	50	,	,	PUNCT
ejpam-393	43	51	respectively	respectively	ADV
ejpam-393	43	52	.	.	PUNCT
ejpam-393	44	1	the	the	DET
ejpam-393	44	2	signature	signature	NOUN
ejpam-393	44	3	includes	include	VERB
ejpam-393	44	4	dimension	dimension	NOUN
ejpam-393	44	5	sort	sort	NOUN
ejpam-393	44	6	constants	constant	VERB
ejpam-393	44	7	iδ	iδ	PROPN
ejpam-393	44	8	for	for	SCONJ
ejpam-393	44	9	each	each	DET
ejpam-393	44	10	i	i	PRON
ejpam-393	44	11	<	<	X
ejpam-393	44	12	ω	ω	INTJ
ejpam-393	44	13	to	to	PART
ejpam-393	44	14	represent	represent	VERB
ejpam-393	44	15	the	the	DET
ejpam-393	44	16	dimensions	dimension	NOUN
ejpam-393	44	17	.	.	PUNCT
ejpam-393	45	1	the	the	DET
ejpam-393	45	2	defining	define	VERB
ejpam-393	45	3	theory	theory	NOUN
ejpam-393	45	4	for	for	ADP
ejpam-393	45	5	nrncaω	nrncaω	PROPN
ejpam-393	45	6	incudes	incus	NOUN
ejpam-393	45	7	sentences	sentence	NOUN
ejpam-393	45	8	demanding	demand	VERB
ejpam-393	45	9	that	that	SCONJ
ejpam-393	45	10	the	the	DET
ejpam-393	45	11	constants	constant	NOUN
ejpam-393	45	12	iδ	iδ	VERB
ejpam-393	45	13	for	for	SCONJ
ejpam-393	45	14	i	i	PRON
ejpam-393	45	15	<	<	PROPN
ejpam-393	45	16	ω	ω	X
ejpam-393	45	17	are	be	AUX
ejpam-393	45	18	distinct	distinct	ADJ
ejpam-393	45	19	and	and	CCONJ
ejpam-393	45	20	that	that	SCONJ
ejpam-393	45	21	the	the	DET
ejpam-393	45	22	last	last	ADJ
ejpam-393	45	23	two	two	NUM
ejpam-393	45	24	sorts	sort	NOUN
ejpam-393	45	25	define	define	VERB
ejpam-393	45	26	a	a	DET
ejpam-393	45	27	cylindric	cylindric	ADJ
ejpam-393	45	28	algebra	algebra	NOUN
ejpam-393	45	29	of	of	ADP
ejpam-393	45	30	dimension	dimension	PROPN
ejpam-393	45	31	ω	ω	PROPN
ejpam-393	45	32	.	.	PUNCT
ejpam-393	46	1	for	for	ADP
ejpam-393	46	2	example	example	NOUN
ejpam-393	46	3	the	the	DET
ejpam-393	46	4	sentence	sentence	NOUN
ejpam-393	46	5	∀xδ	∀xδ	PROPN
ejpam-393	46	6	,	,	PUNCT
ejpam-393	46	7	yδ	yδ	X
ejpam-393	46	8	,	,	PUNCT
ejpam-393	46	9	zδ(d	zδ(d	NUM
ejpam-393	46	10	b(xδ	b(xδ	NOUN
ejpam-393	46	11	,	,	PUNCT
ejpam-393	46	12	yδ	yδ	X
ejpam-393	46	13	)	)	PUNCT
ejpam-393	46	14	=	=	SYM
ejpam-393	46	15	cb(zδ	cb(zδ	PROPN
ejpam-393	46	16	,	,	PUNCT
ejpam-393	46	17	d	d	PROPN
ejpam-393	46	18	b(xδ	b(xδ	PROPN
ejpam-393	46	19	,	,	PUNCT
ejpam-393	46	20	zδ).d	zδ).d	X
ejpam-393	46	21	b(zδ	b(zδ	NOUN
ejpam-393	46	22	,	,	PUNCT
ejpam-393	46	23	yδ	yδ	X
ejpam-393	46	24	)	)	PUNCT
ejpam-393	46	25	)	)	PUNCT
ejpam-393	46	26	)	)	PUNCT
ejpam-393	46	27	represents	represent	VERB
ejpam-393	46	28	the	the	DET
ejpam-393	46	29	cylindric	cylindric	ADJ
ejpam-393	46	30	algebra	algebra	NOUN
ejpam-393	46	31	axiom	axiom	NOUN
ejpam-393	46	32	di	di	X
ejpam-393	46	33	j	j	PROPN
ejpam-393	46	34	=	=	SYM
ejpam-393	46	35	ck(dik.dk	ck(dik.dk	PROPN
ejpam-393	46	36	j	j	PROPN
ejpam-393	46	37	)	)	PUNCT
ejpam-393	46	38	for	for	ADP
ejpam-393	46	39	all	all	DET
ejpam-393	46	40	i	i	PROPN
ejpam-393	46	41	,	,	PUNCT
ejpam-393	46	42	j	j	PROPN
ejpam-393	46	43	,	,	PUNCT
ejpam-393	46	44	k	k	PROPN
ejpam-393	46	45	<	<	X
ejpam-393	46	46	ω	ω	X
ejpam-393	46	47	.	.	PUNCT
ejpam-393	47	1	we	we	PRON
ejpam-393	47	2	have	have	AUX
ejpam-393	47	3	have	have	VERB
ejpam-393	47	4	a	a	DET
ejpam-393	47	5	function	function	NOUN
ejpam-393	47	6	i	i	NOUN
ejpam-393	47	7	b	b	PROPN
ejpam-393	47	8	from	from	ADP
ejpam-393	47	9	sort	sort	NOUN
ejpam-393	47	10	c	c	NOUN
ejpam-393	47	11	to	to	PART
ejpam-393	47	12	sort	sort	VERB
ejpam-393	47	13	b	b	NOUN
ejpam-393	47	14	and	and	CCONJ
ejpam-393	47	15	sentences	sentence	NOUN
ejpam-393	47	16	requiring	require	VERB
ejpam-393	47	17	that	that	SCONJ
ejpam-393	47	18	i	i	PRON
ejpam-393	47	19	b	b	AUX
ejpam-393	47	20	be	be	AUX
ejpam-393	47	21	injective	injective	ADJ
ejpam-393	47	22	and	and	CCONJ
ejpam-393	47	23	to	to	PART
ejpam-393	47	24	respect	respect	VERB
ejpam-393	47	25	the	the	DET
ejpam-393	47	26	n	n	CCONJ
ejpam-393	47	27	dimensional	dimensional	ADJ
ejpam-393	47	28	cylindric	cylindric	ADJ
ejpam-393	47	29	operations	operation	NOUN
ejpam-393	47	30	as	as	SCONJ
ejpam-393	47	31	follows	follow	VERB
ejpam-393	47	32	:	:	PUNCT
ejpam-393	47	33	for	for	ADP
ejpam-393	47	34	all	all	PRON
ejpam-393	47	35	x	x	SYM
ejpam-393	48	1	r	r	NOUN
ejpam-393	49	1	i	i	PRON
ejpam-393	50	1	b(di	b(di	PROPN
ejpam-393	50	2	j	j	NOUN
ejpam-393	50	3	)	)	PUNCT
ejpam-393	51	1	=	=	PUNCT
ejpam-393	51	2	d	d	DET
ejpam-393	51	3	b(iδ	b(iδ	PROPN
ejpam-393	51	4	,	,	PUNCT
ejpam-393	51	5	jδ	jδ	NOUN
ejpam-393	51	6	)	)	PUNCT
ejpam-393	51	7	i	i	PRON
ejpam-393	51	8	b(ci	b(ci	NOUN
ejpam-393	51	9	x	x	SYM
ejpam-393	51	10	r	r	NOUN
ejpam-393	51	11	)	)	PUNCT
ejpam-393	51	12	=	=	SYM
ejpam-393	52	1	cb	cb	PROPN
ejpam-393	52	2	i	i	PRON
ejpam-393	52	3	(	(	PUNCT
ejpam-393	52	4	i	i	PRON
ejpam-393	52	5	b(x	b(x	NOUN
ejpam-393	52	6	)	)	PUNCT
ejpam-393	52	7	)	)	PUNCT
ejpam-393	52	8	.	.	PUNCT
ejpam-393	53	1	finally	finally	ADV
ejpam-393	53	2	we	we	PRON
ejpam-393	53	3	require	require	VERB
ejpam-393	53	4	that	that	SCONJ
ejpam-393	53	5	i	i	PRON
ejpam-393	53	6	b	b	PROPN
ejpam-393	53	7	maps	map	VERB
ejpam-393	53	8	onto	onto	ADP
ejpam-393	53	9	the	the	DET
ejpam-393	53	10	set	set	NOUN
ejpam-393	53	11	of	of	ADP
ejpam-393	53	12	n	n	CCONJ
ejpam-393	53	13	dimensional	dimensional	ADJ
ejpam-393	53	14	elements	element	NOUN
ejpam-393	53	15	∀y	∀y	PROPN
ejpam-393	53	16	b((∀zδ(zδ	b((∀zδ(zδ	PROPN
ejpam-393	53	17	6=	6=	ADP
ejpam-393	53	18	0δ	0δ	NOUN
ejpam-393	53	19	,	,	PUNCT
ejpam-393	53	20	.	.	PUNCT
ejpam-393	53	21	.	.	PUNCT
ejpam-393	53	22	.	.	PUNCT
ejpam-393	54	1	(	(	PUNCT
ejpam-393	54	2	n−	n−	NOUN
ejpam-393	54	3	1)δ→	1)δ→	NUM
ejpam-393	54	4	cb(zδ	cb(zδ	PROPN
ejpam-393	54	5	,	,	PUNCT
ejpam-393	54	6	y	y	PROPN
ejpam-393	54	7	b	b	PROPN
ejpam-393	54	8	)	)	PUNCT
ejpam-393	54	9	=	=	SYM
ejpam-393	55	1	y	y	PROPN
ejpam-393	55	2	b))↔∃x	b))↔∃x	PROPN
ejpam-393	55	3	r(y	r(y	PROPN
ejpam-393	55	4	b	b	PROPN
ejpam-393	55	5	=	=	X
ejpam-393	55	6	i	i	PRON
ejpam-393	55	7	b(x	b(x	VERB
ejpam-393	55	8	r	r	NOUN
ejpam-393	55	9	)	)	PUNCT
ejpam-393	55	10	)	)	PUNCT
ejpam-393	55	11	)	)	PUNCT
ejpam-393	55	12	.	.	PUNCT
ejpam-393	56	1	for	for	ADP
ejpam-393	56	2	a	a	DET
ejpam-393	56	3	∈	∈	PROPN
ejpam-393	56	4	can	can	AUX
ejpam-393	56	5	,	,	PUNCT
ejpam-393	56	6	rd3a	rd3a	NOUN
ejpam-393	56	7	denotes	denote	VERB
ejpam-393	56	8	the	the	DET
ejpam-393	56	9	ca3	ca3	PROPN
ejpam-393	56	10	obtained	obtain	VERB
ejpam-393	56	11	from	from	ADP
ejpam-393	56	12	a	a	PRON
ejpam-393	56	13	by	by	ADP
ejpam-393	56	14	discarding	discard	VERB
ejpam-393	56	15	all	all	DET
ejpam-393	56	16	operations	operation	NOUN
ejpam-393	56	17	indexed	index	VERB
ejpam-393	56	18	by	by	ADP
ejpam-393	56	19	indices	index	NOUN
ejpam-393	56	20	in	in	ADP
ejpam-393	56	21	n	n	PRON
ejpam-393	56	22	∼	∼	NOUN
ejpam-393	56	23	3	3	NUM
ejpam-393	56	24	.	.	PUNCT
ejpam-393	57	1	dfn	dfn	NOUN
ejpam-393	57	2	denotes	denote	VERB
ejpam-393	57	3	the	the	DET
ejpam-393	57	4	class	class	NOUN
ejpam-393	57	5	of	of	ADP
ejpam-393	57	6	diagonal	diagonal	ADJ
ejpam-393	57	7	free	free	ADJ
ejpam-393	57	8	cylindric	cylindric	ADJ
ejpam-393	57	9	algebras	algebra	NOUN
ejpam-393	57	10	.	.	PUNCT
ejpam-393	58	1	rdd	rdd	PROPN
ejpam-393	58	2	f	f	PROPN
ejpam-393	58	3	a	a	DET
ejpam-393	58	4	denotes	denote	NOUN
ejpam-393	58	5	the	the	DET
ejpam-393	58	6	dfn	dfn	NOUN
ejpam-393	58	7	obtained	obtain	VERB
ejpam-393	58	8	from	from	ADP
ejpam-393	58	9	a	a	PRON
ejpam-393	58	10	by	by	ADP
ejpam-393	58	11	deleting	delete	VERB
ejpam-393	58	12	all	all	DET
ejpam-393	58	13	diagonal	diagonal	ADJ
ejpam-393	58	14	elements	element	NOUN
ejpam-393	58	15	.	.	PUNCT
ejpam-393	59	1	to	to	PART
ejpam-393	59	2	prove	prove	VERB
ejpam-393	59	3	the	the	DET
ejpam-393	59	4	non	non	ADJ
ejpam-393	59	5	-	-	ADJ
ejpam-393	59	6	finite	finite	ADJ
ejpam-393	59	7	axiomatizability	axiomatizability	NOUN
ejpam-393	59	8	result	result	NOUN
ejpam-393	59	9	we	we	PRON
ejpam-393	59	10	use	use	VERB
ejpam-393	59	11	monk	monk	NOUN
ejpam-393	59	12	’s	’s	PART
ejpam-393	59	13	algebras	algebras	PROPN
ejpam-393	59	14	.	.	PUNCT
ejpam-393	60	1	for	for	ADP
ejpam-393	60	2	3	3	NUM
ejpam-393	60	3	≤	≤	NOUN
ejpam-393	60	4	n	n	CCONJ
ejpam-393	60	5	,	,	PUNCT
ejpam-393	60	6	i	i	PRON
ejpam-393	60	7	<	<	X
ejpam-393	60	8	ω	ω	PROPN
ejpam-393	60	9	,	,	PUNCT
ejpam-393	60	10	with	with	ADP
ejpam-393	60	11	n−	n−	NOUN
ejpam-393	60	12	1	1	NUM
ejpam-393	60	13	≤	≤	PUNCT
ejpam-393	60	14	i	i	PRON
ejpam-393	60	15	,	,	PUNCT
ejpam-393	60	16	cn	cn	PROPN
ejpam-393	60	17	,	,	PUNCT
ejpam-393	60	18	i	i	PRON
ejpam-393	60	19	denotes	denote	VERB
ejpam-393	60	20	the	the	PRON
ejpam-393	60	21	can	can	AUX
ejpam-393	60	22	associated	associate	VERB
ejpam-393	60	23	with	with	ADP
ejpam-393	60	24	the	the	DET
ejpam-393	60	25	cylindric	cylindric	ADJ
ejpam-393	60	26	atom	atom	NOUN
ejpam-393	60	27	structure	structure	NOUN
ejpam-393	60	28	as	as	SCONJ
ejpam-393	60	29	defined	define	VERB
ejpam-393	60	30	on	on	ADP
ejpam-393	60	31	p.	p.	PROPN
ejpam-393	60	32	95	95	NUM
ejpam-393	60	33	of	of	ADP
ejpam-393	60	34	[	[	X
ejpam-393	60	35	11	11	NUM
ejpam-393	60	36	]	]	PUNCT
ejpam-393	60	37	.	.	PUNCT
ejpam-393	61	1	then	then	ADV
ejpam-393	61	2	by	by	ADP
ejpam-393	61	3	[	[	X
ejpam-393	61	4	11	11	NUM
ejpam-393	61	5	,	,	PUNCT
ejpam-393	61	6	3.2.79	3.2.79	NUM
ejpam-393	61	7	]	]	PUNCT
ejpam-393	61	8	for	for	ADP
ejpam-393	61	9	3≤	3≤	NUM
ejpam-393	61	10	n	n	CCONJ
ejpam-393	61	11	,	,	PUNCT
ejpam-393	61	12	and	and	CCONJ
ejpam-393	61	13	j	j	PROPN
ejpam-393	61	14	<	<	X
ejpam-393	61	15	ω	ω	PROPN
ejpam-393	61	16	,	,	PUNCT
ejpam-393	61	17	rd3cn	rd3cn	NUM
ejpam-393	61	18	,	,	PUNCT
ejpam-393	61	19	n+	n+	PUNCT
ejpam-393	61	20	j	j	PROPN
ejpam-393	61	21	can	can	AUX
ejpam-393	61	22	be	be	AUX
ejpam-393	61	23	neatly	neatly	ADV
ejpam-393	61	24	embedded	embed	VERB
ejpam-393	61	25	in	in	ADP
ejpam-393	61	26	a	a	DET
ejpam-393	61	27	ca3	ca3	NOUN
ejpam-393	61	28	+	+	X
ejpam-393	61	29	j+1	j+1	NUM
ejpam-393	61	30	.	.	PUNCT
ejpam-393	62	1	(	(	PUNCT
ejpam-393	62	2	1	1	NUM
ejpam-393	62	3	)	)	PUNCT
ejpam-393	62	4	by	by	ADP
ejpam-393	62	5	[	[	X
ejpam-393	62	6	11	11	NUM
ejpam-393	62	7	,	,	PUNCT
ejpam-393	62	8	3.2.84	3.2.84	PROPN
ejpam-393	62	9	]	]	PUNCT
ejpam-393	62	10	)	)	PUNCT
ejpam-393	62	11	we	we	PRON
ejpam-393	62	12	have	have	VERB
ejpam-393	62	13	for	for	ADP
ejpam-393	62	14	every	every	DET
ejpam-393	62	15	j	j	PROPN
ejpam-393	62	16	∈ω	∈ω	NOUN
ejpam-393	62	17	,	,	PUNCT
ejpam-393	62	18	there	there	PRON
ejpam-393	62	19	is	be	VERB
ejpam-393	62	20	an	an	DET
ejpam-393	62	21	3≤	3≤	NUM
ejpam-393	62	22	n	n	NOUN
ejpam-393	62	23	such	such	ADJ
ejpam-393	62	24	that	that	SCONJ
ejpam-393	62	25	rdd	rdd	PROPN
ejpam-393	62	26	f	f	PROPN
ejpam-393	62	27	rd3c	rd3c	PROPN
ejpam-393	62	28	n	n	CCONJ
ejpam-393	62	29	,	,	PUNCT
ejpam-393	62	30	n+	n+	PUNCT
ejpam-393	62	31	j	j	PROPN
ejpam-393	62	32	is	be	AUX
ejpam-393	62	33	a	a	DET
ejpam-393	62	34	non	non	ADJ
ejpam-393	62	35	-	-	ADJ
ejpam-393	62	36	representable	representable	ADJ
ejpam-393	62	37	df3	df3	NOUN
ejpam-393	62	38	.	.	PUNCT
ejpam-393	63	1	t.	t.	PROPN
ejpam-393	63	2	ahmed	ahmed	PROPN
ejpam-393	63	3	/	/	SYM
ejpam-393	63	4	eur	eur	PROPN
ejpam-393	63	5	.	.	PUNCT
ejpam-393	64	1	j.	j.	PROPN
ejpam-393	64	2	pure	pure	PROPN
ejpam-393	64	3	appl	appl	PROPN
ejpam-393	64	4	.	.	PROPN
ejpam-393	64	5	math	math	PROPN
ejpam-393	64	6	,	,	PUNCT
ejpam-393	64	7	3	3	NUM
ejpam-393	64	8	(	(	PUNCT
ejpam-393	64	9	2010	2010	NUM
ejpam-393	64	10	)	)	PUNCT
ejpam-393	64	11	,	,	PUNCT
ejpam-393	64	12	853	853	NUM
ejpam-393	64	13	-	-	SYM
ejpam-393	64	14	880	880	NUM
ejpam-393	64	15	855	855	NUM
ejpam-393	64	16	(	(	PUNCT
ejpam-393	64	17	2	2	NUM
ejpam-393	64	18	)	)	PUNCT
ejpam-393	64	19	now	now	ADV
ejpam-393	64	20	suppose	suppose	VERB
ejpam-393	64	21	m	m	VERB
ejpam-393	64	22	∈	∈	PROPN
ejpam-393	64	23	ω	ω	PROPN
ejpam-393	64	24	.	.	PUNCT
ejpam-393	65	1	by	by	ADP
ejpam-393	65	2	(	(	PUNCT
ejpam-393	65	3	2	2	NUM
ejpam-393	65	4	)	)	PUNCT
ejpam-393	65	5	,	,	PUNCT
ejpam-393	65	6	choose	choose	VERB
ejpam-393	65	7	j	j	PROPN
ejpam-393	65	8	∈	∈	PROPN
ejpam-393	65	9	ω	ω	PROPN
ejpam-393	65	10	∼	∼	NOUN
ejpam-393	65	11	3	3	NUM
ejpam-393	65	12	so	so	SCONJ
ejpam-393	65	13	that	that	SCONJ
ejpam-393	65	14	rdd	rdd	VERB
ejpam-393	65	15	f	f	PROPN
ejpam-393	65	16	rd3c	rd3c	PROPN
ejpam-393	65	17	j	j	PROPN
ejpam-393	65	18	,	,	PUNCT
ejpam-393	65	19	j+m+n−4	j+m+n−4	NOUN
ejpam-393	65	20	is	be	AUX
ejpam-393	65	21	a	a	DET
ejpam-393	65	22	non	non	ADJ
ejpam-393	65	23	-	-	ADJ
ejpam-393	65	24	representable	representable	ADJ
ejpam-393	65	25	df3	df3	NOUN
ejpam-393	65	26	.	.	PUNCT
ejpam-393	66	1	by	by	ADP
ejpam-393	66	2	(	(	PUNCT
ejpam-393	66	3	1	1	X
ejpam-393	66	4	)	)	PUNCT
ejpam-393	66	5	we	we	PRON
ejpam-393	66	6	have	have	VERB
ejpam-393	66	7	rdd	rdd	NOUN
ejpam-393	66	8	f	f	PROPN
ejpam-393	66	9	rd3c	rd3c	PROPN
ejpam-393	66	10	j	j	PROPN
ejpam-393	66	11	,	,	PUNCT
ejpam-393	66	12	j+m+n−4	j+m+n−4	NOUN
ejpam-393	66	13	⊆nr3bm	⊆nr3bm	NOUN
ejpam-393	66	14	,	,	PUNCT
ejpam-393	66	15	for	for	ADP
ejpam-393	66	16	some	some	PRON
ejpam-393	66	17	b	b	PROPN
ejpam-393	66	18	∈	∈	PROPN
ejpam-393	66	19	can+m	can+m	PROPN
ejpam-393	66	20	.	.	PUNCT
ejpam-393	67	1	put	put	PROPN
ejpam-393	67	2	am	be	AUX
ejpam-393	67	3	=	=	SYM
ejpam-393	67	4	nrnbm	nrnbm	ADJ
ejpam-393	67	5	.	.	PUNCT
ejpam-393	68	1	rdd	rdd	PROPN
ejpam-393	68	2	f	f	PROPN
ejpam-393	68	3	am	be	AUX
ejpam-393	68	4	is	be	AUX
ejpam-393	68	5	not	not	PART
ejpam-393	68	6	representable	representable	ADJ
ejpam-393	68	7	,	,	PUNCT
ejpam-393	68	8	a	a	DET
ejpam-393	68	9	friotri	friotri	NOUN
ejpam-393	68	10	,	,	PUNCT
ejpam-393	68	11	am	be	AUX
ejpam-393	68	12	/∈	/∈	NOUN
ejpam-393	68	13	rcan	rcan	ADJ
ejpam-393	68	14	,	,	PUNCT
ejpam-393	68	15	for	for	ADP
ejpam-393	68	16	else	else	ADV
ejpam-393	68	17	its	its	PRON
ejpam-393	68	18	df	df	PROPN
ejpam-393	68	19	reduct	reduct	NOUN
ejpam-393	68	20	would	would	AUX
ejpam-393	68	21	be	be	AUX
ejpam-393	68	22	representable	representable	ADJ
ejpam-393	68	23	.	.	PUNCT
ejpam-393	69	1	therefore	therefore	ADV
ejpam-393	69	2	am	be	AUX
ejpam-393	69	3	/∈	/∈	PUNCT
ejpam-393	70	1	e	e	X
ejpam-393	70	2	lnrncaω	lnrncaω	PROPN
ejpam-393	70	3	.	.	PUNCT
ejpam-393	71	1	now	now	ADV
ejpam-393	71	2	let	let	VERB
ejpam-393	71	3	cm	cm	NOUN
ejpam-393	71	4	be	be	AUX
ejpam-393	71	5	an	an	DET
ejpam-393	71	6	algebra	algebra	NOUN
ejpam-393	71	7	similar	similar	ADJ
ejpam-393	71	8	to	to	ADP
ejpam-393	71	9	caω	caω	PROPN
ejpam-393	71	10	’s	’	VERB
ejpam-393	71	11	such	such	ADJ
ejpam-393	71	12	that	that	SCONJ
ejpam-393	71	13	bm	bm	PROPN
ejpam-393	71	14	=	=	PROPN
ejpam-393	71	15	rdn+mcm	rdn+mcm	PROPN
ejpam-393	71	16	.	.	PUNCT
ejpam-393	72	1	then	then	ADV
ejpam-393	72	2	am	be	AUX
ejpam-393	72	3	=	=	SYM
ejpam-393	72	4	nrncm	nrncm	ADJ
ejpam-393	72	5	.	.	PUNCT
ejpam-393	73	1	let	let	VERB
ejpam-393	73	2	f	f	PRON
ejpam-393	73	3	be	be	AUX
ejpam-393	73	4	a	a	DET
ejpam-393	73	5	non	non	ADJ
ejpam-393	73	6	-	-	ADJ
ejpam-393	73	7	principal	principal	ADJ
ejpam-393	73	8	ultrafilter	ultrafilter	NOUN
ejpam-393	73	9	on	on	ADP
ejpam-393	73	10	ω	ω	PROPN
ejpam-393	73	11	.	.	PUNCT
ejpam-393	74	1	then	then	ADV
ejpam-393	74	2	∏	∏	NUM
ejpam-393	74	3	m∈ω	m∈ω	NOUN
ejpam-393	74	4	am	am	NOUN
ejpam-393	74	5	/	/	SYM
ejpam-393	74	6	f	f	NOUN
ejpam-393	74	7	=	=	SYM
ejpam-393	74	8	∏	∏	PROPN
ejpam-393	74	9	m∈ω	m∈ω	NOUN
ejpam-393	74	10	(	(	PUNCT
ejpam-393	74	11	nrncm)/f	nrncm)/f	NOUN
ejpam-393	74	12	=	=	SYM
ejpam-393	74	13	nrn	nrn	PROPN
ejpam-393	74	14	(	(	PUNCT
ejpam-393	74	15	∏	∏	PROPN
ejpam-393	74	16	m∈ω	m∈ω	NOUN
ejpam-393	74	17	cm	cm	NOUN
ejpam-393	74	18	/	/	SYM
ejpam-393	74	19	f	f	NOUN
ejpam-393	74	20	)	)	PUNCT
ejpam-393	74	21	but	but	CCONJ
ejpam-393	74	22	∏	∏	PROPN
ejpam-393	74	23	m∈ωcm	m∈ωcm	PROPN
ejpam-393	74	24	/	/	SYM
ejpam-393	74	25	f	f	PROPN
ejpam-393	74	26	∈	∈	PROPN
ejpam-393	74	27	caω	caω	PROPN
ejpam-393	74	28	.	.	PUNCT
ejpam-393	75	1	hence	hence	ADV
ejpam-393	75	2	can	can	AUX
ejpam-393	75	3	∼	∼	VERB
ejpam-393	75	4	elnrncaω	elnrncaω	PROPN
ejpam-393	75	5	is	be	AUX
ejpam-393	75	6	not	not	PART
ejpam-393	75	7	closed	close	VERB
ejpam-393	75	8	under	under	ADP
ejpam-393	75	9	ultraproducts	ultraproduct	NOUN
ejpam-393	75	10	.	.	PUNCT
ejpam-393	76	1	it	it	PRON
ejpam-393	76	2	follows	follow	VERB
ejpam-393	76	3	that	that	SCONJ
ejpam-393	76	4	the	the	DET
ejpam-393	76	5	latter	latter	ADJ
ejpam-393	76	6	class	class	NOUN
ejpam-393	76	7	is	be	AUX
ejpam-393	76	8	not	not	PART
ejpam-393	76	9	finitely	finitely	ADV
ejpam-393	76	10	axiomatizable	axiomatizable	ADJ
ejpam-393	76	11	.	.	PUNCT
ejpam-393	77	1	in	in	ADP
ejpam-393	77	2	[	[	X
ejpam-393	77	3	18	18	NUM
ejpam-393	77	4	]	]	X
ejpam-393	77	5	it	it	PRON
ejpam-393	77	6	is	be	AUX
ejpam-393	77	7	proved	prove	VERB
ejpam-393	77	8	that	that	SCONJ
ejpam-393	77	9	for	for	ADP
ejpam-393	77	10	1	1	NUM
ejpam-393	77	11	<	<	X
ejpam-393	77	12	α	α	X
ejpam-393	77	13	<	<	X
ejpam-393	77	14	β	β	X
ejpam-393	77	15	,	,	PUNCT
ejpam-393	77	16	elnrαcaβ	elnrαcaβ	PROPN
ejpam-393	77	17	⊂	⊂	PROPN
ejpam-393	77	18	snrαcaβ	snrαcaβ	PROPN
ejpam-393	77	19	.	.	PUNCT
ejpam-393	78	1	from	from	ADP
ejpam-393	78	2	the	the	DET
ejpam-393	78	3	above	above	ADJ
ejpam-393	78	4	proof	proof	NOUN
ejpam-393	78	5	it	it	PRON
ejpam-393	78	6	follows	follow	VERB
ejpam-393	78	7	that	that	PRON
ejpam-393	78	8	corollary	corollary	ADJ
ejpam-393	78	9	1	1	X
ejpam-393	78	10	.	.	PUNCT
ejpam-393	79	1	let	let	VERB
ejpam-393	79	2	k	k	PRON
ejpam-393	79	3	be	be	AUX
ejpam-393	79	4	any	any	DET
ejpam-393	79	5	class	class	NOUN
ejpam-393	79	6	such	such	ADJ
ejpam-393	79	7	that	that	SCONJ
ejpam-393	80	1	nrncaω	nrncaω	PROPN
ejpam-393	80	2	⊆	⊆	NUM
ejpam-393	80	3	k	k	NOUN
ejpam-393	80	4	⊆	⊆	NUM
ejpam-393	80	5	rcan	rcan	NOUN
ejpam-393	80	6	.	.	PUNCT
ejpam-393	81	1	then	then	ADV
ejpam-393	81	2	e	e	X
ejpam-393	81	3	lk	lk	PROPN
ejpam-393	81	4	is	be	AUX
ejpam-393	81	5	not	not	PART
ejpam-393	81	6	finitely	finitely	ADV
ejpam-393	81	7	axiomatizable	axiomatizable	ADJ
ejpam-393	81	8	for	for	ADP
ejpam-393	81	9	n	n	X
ejpam-393	81	10	>	>	X
ejpam-393	81	11	2	2	NUM
ejpam-393	81	12	the	the	DET
ejpam-393	81	13	addition	addition	NOUN
ejpam-393	81	14	of	of	ADP
ejpam-393	81	15	finitely	finitely	ADV
ejpam-393	81	16	many	many	ADJ
ejpam-393	81	17	first	first	ADJ
ejpam-393	81	18	order	order	NOUN
ejpam-393	81	19	definable	definable	ADJ
ejpam-393	81	20	operations	operation	NOUN
ejpam-393	81	21	does	do	AUX
ejpam-393	81	22	not	not	PART
ejpam-393	81	23	remedy	remedy	VERB
ejpam-393	81	24	the	the	DET
ejpam-393	81	25	non	non	ADJ
ejpam-393	81	26	-	-	ADJ
ejpam-393	81	27	finite	finite	ADJ
ejpam-393	81	28	axiomatizability	axiomatizability	NOUN
ejpam-393	81	29	result	result	NOUN
ejpam-393	81	30	for	for	ADP
ejpam-393	81	31	rcan	rcan	ADJ
ejpam-393	81	32	,	,	PUNCT
ejpam-393	81	33	as	as	SCONJ
ejpam-393	81	34	proved	prove	VERB
ejpam-393	81	35	by	by	ADP
ejpam-393	81	36	biro	biro	PROPN
ejpam-393	81	37	.	.	PUNCT
ejpam-393	82	1	first	first	ADJ
ejpam-393	82	2	order	order	NOUN
ejpam-393	82	3	definable	definable	ADJ
ejpam-393	82	4	operations	operation	NOUN
ejpam-393	82	5	are	be	AUX
ejpam-393	82	6	those	those	DET
ejpam-393	82	7	operations	operation	NOUN
ejpam-393	82	8	that	that	PRON
ejpam-393	82	9	can	can	AUX
ejpam-393	82	10	be	be	AUX
ejpam-393	82	11	defined	define	VERB
ejpam-393	82	12	using	use	VERB
ejpam-393	82	13	spare	spare	ADJ
ejpam-393	82	14	dimensions	dimension	NOUN
ejpam-393	82	15	,	,	PUNCT
ejpam-393	82	16	and	and	CCONJ
ejpam-393	82	17	hence	hence	ADV
ejpam-393	82	18	the	the	DET
ejpam-393	82	19	notion	notion	NOUN
ejpam-393	82	20	of	of	ADP
ejpam-393	82	21	neat	neat	ADJ
ejpam-393	82	22	reducts	reduct	NOUN
ejpam-393	82	23	are	be	AUX
ejpam-393	82	24	appropriate	appropriate	ADJ
ejpam-393	82	25	for	for	ADP
ejpam-393	82	26	handing	hand	VERB
ejpam-393	82	27	them	they	PRON
ejpam-393	82	28	.	.	PUNCT
ejpam-393	83	1	a	a	DET
ejpam-393	83	2	non	non	ADJ
ejpam-393	83	3	-	-	ADJ
ejpam-393	83	4	trivial	trivial	ADJ
ejpam-393	83	5	question	question	NOUN
ejpam-393	83	6	that	that	PRON
ejpam-393	83	7	involves	involve	VERB
ejpam-393	83	8	the	the	DET
ejpam-393	83	9	class	class	NOUN
ejpam-393	83	10	nrncaω	nrncaω	INTJ
ejpam-393	83	11	in	in	ADP
ejpam-393	83	12	an	an	DET
ejpam-393	83	13	essential	essential	ADJ
ejpam-393	83	14	way	way	NOUN
ejpam-393	83	15	,	,	PUNCT
ejpam-393	83	16	is	be	AUX
ejpam-393	83	17	whether	whether	SCONJ
ejpam-393	83	18	we	we	PRON
ejpam-393	83	19	can	can	AUX
ejpam-393	83	20	expand	expand	VERB
ejpam-393	83	21	the	the	DET
ejpam-393	83	22	signature	signature	NOUN
ejpam-393	83	23	of	of	ADP
ejpam-393	83	24	cylindric	cylindric	ADJ
ejpam-393	83	25	algebras	algebra	NOUN
ejpam-393	83	26	by	by	ADP
ejpam-393	83	27	extra	extra	ADJ
ejpam-393	83	28	natural	natural	ADJ
ejpam-393	83	29	operations	operation	NOUN
ejpam-393	83	30	on	on	ADP
ejpam-393	83	31	n	n	CCONJ
ejpam-393	83	32	-	-	PUNCT
ejpam-393	83	33	ary	ary	NOUN
ejpam-393	83	34	relations	relation	NOUN
ejpam-393	83	35	so	so	SCONJ
ejpam-393	83	36	that	that	SCONJ
ejpam-393	83	37	if	if	SCONJ
ejpam-393	83	38	a	a	DET
ejpam-393	83	39	∈	∈	PROPN
ejpam-393	83	40	csn	csn	NOUN
ejpam-393	83	41	and	and	CCONJ
ejpam-393	83	42	is	be	AUX
ejpam-393	83	43	closed	close	VERB
ejpam-393	83	44	under	under	ADP
ejpam-393	83	45	these	these	DET
ejpam-393	83	46	operations	operation	NOUN
ejpam-393	83	47	then	then	ADV
ejpam-393	83	48	this	this	DET
ejpam-393	83	49	forces	force	VERB
ejpam-393	83	50	a	a	PRON
ejpam-393	83	51	to	to	PART
ejpam-393	83	52	be	be	AUX
ejpam-393	83	53	in	in	ADP
ejpam-393	83	54	the	the	DET
ejpam-393	83	55	class	class	NOUN
ejpam-393	83	56	nrncaω	nrncaω	PROPN
ejpam-393	83	57	.	.	PUNCT
ejpam-393	84	1	(	(	PUNCT
ejpam-393	84	2	for	for	ADP
ejpam-393	84	3	example	example	NOUN
ejpam-393	84	4	,	,	PUNCT
ejpam-393	84	5	the	the	DET
ejpam-393	84	6	polyadic	polyadic	ADJ
ejpam-393	84	7	operations	operation	NOUN
ejpam-393	84	8	are	be	AUX
ejpam-393	84	9	not	not	PART
ejpam-393	84	10	enough	enough	ADJ
ejpam-393	84	11	.	.	PUNCT
ejpam-393	84	12	)	)	PUNCT
ejpam-393	85	1	the	the	DET
ejpam-393	85	2	class	class	NOUN
ejpam-393	85	3	nrncaω	nrncaω	PROPN
ejpam-393	85	4	contains	contain	VERB
ejpam-393	85	5	all	all	DET
ejpam-393	85	6	first	first	ADJ
ejpam-393	85	7	order	order	NOUN
ejpam-393	85	8	definable	definable	ADJ
ejpam-393	85	9	operations	operation	NOUN
ejpam-393	85	10	,	,	PUNCT
ejpam-393	85	11	so	so	CCONJ
ejpam-393	85	12	the	the	DET
ejpam-393	85	13	question	question	NOUN
ejpam-393	85	14	can	can	AUX
ejpam-393	85	15	be	be	AUX
ejpam-393	85	16	reformulated	reformulate	VERB
ejpam-393	85	17	as	as	ADP
ejpam-393	85	18	to	to	ADP
ejpam-393	85	19	whether	whether	SCONJ
ejpam-393	85	20	one	one	PRON
ejpam-393	85	21	can	can	AUX
ejpam-393	85	22	capture	capture	VERB
ejpam-393	85	23	all	all	DET
ejpam-393	85	24	first	first	ADJ
ejpam-393	85	25	order	order	NOUN
ejpam-393	85	26	definable	definable	ADJ
ejpam-393	85	27	operations	operation	NOUN
ejpam-393	85	28	using	use	VERB
ejpam-393	85	29	a	a	DET
ejpam-393	85	30	finite	finite	ADJ
ejpam-393	85	31	set	set	NOUN
ejpam-393	85	32	of	of	ADP
ejpam-393	85	33	operations	operation	NOUN
ejpam-393	85	34	.	.	PUNCT
ejpam-393	86	1	this	this	PRON
ejpam-393	86	2	is	be	AUX
ejpam-393	86	3	strongly	strongly	ADV
ejpam-393	86	4	related	relate	VERB
ejpam-393	86	5	to	to	ADP
ejpam-393	86	6	the	the	DET
ejpam-393	86	7	finitizability	finitizability	NOUN
ejpam-393	86	8	problem	problem	NOUN
ejpam-393	86	9	[	[	X
ejpam-393	86	10	48	48	NUM
ejpam-393	86	11	]	]	PUNCT
ejpam-393	86	12	in	in	ADP
ejpam-393	86	13	algebraic	algebraic	ADJ
ejpam-393	86	14	logic	logic	NOUN
ejpam-393	86	15	.	.	PUNCT
ejpam-393	87	1	next	next	ADV
ejpam-393	87	2	we	we	PRON
ejpam-393	87	3	characterize	characterize	VERB
ejpam-393	87	4	the	the	DET
ejpam-393	87	5	class	class	NOUN
ejpam-393	87	6	nrncaω	nrncaω	ADV
ejpam-393	87	7	using	use	VERB
ejpam-393	87	8	games	game	NOUN
ejpam-393	87	9	.	.	PUNCT
ejpam-393	88	1	since	since	SCONJ
ejpam-393	88	2	games	game	NOUN
ejpam-393	88	3	go	go	VERB
ejpam-393	88	4	deeper	deeply	ADV
ejpam-393	88	5	into	into	ADP
ejpam-393	88	6	the	the	DET
ejpam-393	88	7	analysis	analysis	NOUN
ejpam-393	88	8	,	,	PUNCT
ejpam-393	88	9	they	they	PRON
ejpam-393	88	10	could	could	AUX
ejpam-393	88	11	shed	shed	VERB
ejpam-393	88	12	light	light	NOUN
ejpam-393	88	13	on	on	ADP
ejpam-393	88	14	the	the	DET
ejpam-393	88	15	possible	possible	ADJ
ejpam-393	88	16	choice	choice	NOUN
ejpam-393	88	17	of	of	ADP
ejpam-393	88	18	such	such	ADJ
ejpam-393	88	19	operations	operation	NOUN
ejpam-393	88	20	.	.	PUNCT
ejpam-393	89	1	for	for	ADP
ejpam-393	89	2	that	that	PRON
ejpam-393	89	3	,	,	PUNCT
ejpam-393	89	4	we	we	PRON
ejpam-393	89	5	need	need	VERB
ejpam-393	89	6	some	some	DET
ejpam-393	89	7	preparations	preparation	NOUN
ejpam-393	89	8	.	.	PUNCT
ejpam-393	90	1	we	we	PRON
ejpam-393	90	2	use	use	VERB
ejpam-393	90	3	“	"	PUNCT
ejpam-393	90	4	cylindric	cylindric	ADJ
ejpam-393	90	5	algebra	algebra	NOUN
ejpam-393	90	6	”	"	PUNCT
ejpam-393	90	7	games	game	NOUN
ejpam-393	90	8	that	that	PRON
ejpam-393	90	9	are	be	AUX
ejpam-393	90	10	analogues	analogue	NOUN
ejpam-393	90	11	to	to	ADP
ejpam-393	90	12	certain	certain	ADJ
ejpam-393	90	13	“	"	PUNCT
ejpam-393	90	14	relation	relation	NOUN
ejpam-393	90	15	algebra	algebra	NOUN
ejpam-393	90	16	”	"	PUNCT
ejpam-393	90	17	games	game	NOUN
ejpam-393	90	18	used	use	VERB
ejpam-393	90	19	by	by	ADP
ejpam-393	90	20	robin	robin	PROPN
ejpam-393	90	21	hirsch	hirsch	PROPN
ejpam-393	90	22	in	in	ADP
ejpam-393	90	23	[	[	X
ejpam-393	90	24	7	7	NUM
ejpam-393	90	25	]	]	PUNCT
ejpam-393	90	26	.	.	PUNCT
ejpam-393	91	1	in	in	ADP
ejpam-393	91	2	[	[	X
ejpam-393	91	3	7	7	X
ejpam-393	91	4	]	]	PUNCT
ejpam-393	91	5	robin	robin	PROPN
ejpam-393	91	6	hirsch	hirsch	PROPN
ejpam-393	91	7	studies	study	NOUN
ejpam-393	91	8	quite	quite	ADV
ejpam-393	91	9	extensively	extensively	ADV
ejpam-393	91	10	the	the	DET
ejpam-393	91	11	class	class	NOUN
ejpam-393	91	12	racan	racan	NOUN
ejpam-393	91	13	of	of	ADP
ejpam-393	91	14	relation	relation	NOUN
ejpam-393	91	15	algebra	algebra	NOUN
ejpam-393	91	16	reducts	reduct	NOUN
ejpam-393	91	17	of	of	ADP
ejpam-393	91	18	cylindric	cylindric	ADJ
ejpam-393	91	19	algebras	algebra	NOUN
ejpam-393	91	20	of	of	ADP
ejpam-393	91	21	dimension	dimension	NOUN
ejpam-393	91	22	n.	n.	PROPN
ejpam-393	91	23	this	this	DET
ejpam-393	91	24	class	class	NOUN
ejpam-393	91	25	was	be	AUX
ejpam-393	91	26	studied	study	VERB
ejpam-393	91	27	by	by	ADP
ejpam-393	91	28	many	many	ADJ
ejpam-393	91	29	authors	author	NOUN
ejpam-393	91	30	,	,	PUNCT
ejpam-393	91	31	to	to	PART
ejpam-393	91	32	mention	mention	VERB
ejpam-393	91	33	a	a	DET
ejpam-393	91	34	few	few	ADJ
ejpam-393	91	35	,	,	PUNCT
ejpam-393	91	36	maddux	maddux	PROPN
ejpam-393	91	37	,	,	PUNCT
ejpam-393	91	38	simon	simon	PROPN
ejpam-393	91	39	and	and	CCONJ
ejpam-393	91	40	nemeti	nemeti	NOUN
ejpam-393	91	41	.	.	PUNCT
ejpam-393	92	1	references	reference	NOUN
ejpam-393	92	2	for	for	ADP
ejpam-393	92	3	their	their	PRON
ejpam-393	92	4	work	work	NOUN
ejpam-393	92	5	can	can	AUX
ejpam-393	92	6	be	be	AUX
ejpam-393	92	7	found	find	VERB
ejpam-393	92	8	in	in	ADP
ejpam-393	92	9	the	the	DET
ejpam-393	92	10	most	most	ADV
ejpam-393	92	11	recent	recent	ADJ
ejpam-393	92	12	reference	reference	NOUN
ejpam-393	92	13	[	[	X
ejpam-393	92	14	7	7	NUM
ejpam-393	92	15	]	]	PUNCT
ejpam-393	92	16	.	.	PUNCT
ejpam-393	93	1	our	our	PRON
ejpam-393	93	2	treatment	treatment	NOUN
ejpam-393	93	3	in	in	ADP
ejpam-393	93	4	this	this	DET
ejpam-393	93	5	part	part	NOUN
ejpam-393	93	6	follows	follow	VERB
ejpam-393	93	7	very	very	ADV
ejpam-393	93	8	closely	closely	ADV
ejpam-393	93	9	[	[	X
ejpam-393	93	10	7	7	NUM
ejpam-393	93	11	]	]	PUNCT
ejpam-393	93	12	.	.	PUNCT
ejpam-393	94	1	definition	definition	NOUN
ejpam-393	94	2	1	1	NUM
ejpam-393	94	3	.	.	PUNCT
ejpam-393	95	1	let	let	VERB
ejpam-393	95	2	n	n	PRON
ejpam-393	95	3	be	be	AUX
ejpam-393	95	4	an	an	DET
ejpam-393	95	5	ordinal	ordinal	ADJ
ejpam-393	95	6	.	.	PUNCT
ejpam-393	96	1	an	an	DET
ejpam-393	96	2	s	s	NOUN
ejpam-393	96	3	word	word	NOUN
ejpam-393	96	4	is	be	AUX
ejpam-393	96	5	a	a	DET
ejpam-393	96	6	finite	finite	ADJ
ejpam-393	96	7	string	string	NOUN
ejpam-393	96	8	of	of	ADP
ejpam-393	96	9	substitutions	substitution	NOUN
ejpam-393	96	10	(	(	PUNCT
ejpam-393	96	11	s	s	X
ejpam-393	96	12	j	j	PROPN
ejpam-393	96	13	i	i	PROPN
ejpam-393	96	14	)	)	PUNCT
ejpam-393	96	15	,	,	PUNCT
ejpam-393	96	16	a	a	DET
ejpam-393	96	17	c	c	NOUN
ejpam-393	96	18	word	word	NOUN
ejpam-393	96	19	is	be	AUX
ejpam-393	96	20	a	a	DET
ejpam-393	96	21	finite	finite	ADJ
ejpam-393	96	22	string	string	NOUN
ejpam-393	96	23	of	of	ADP
ejpam-393	96	24	cylindrifications	cylindrification	NOUN
ejpam-393	96	25	(	(	PUNCT
ejpam-393	96	26	ck	ck	NOUN
ejpam-393	96	27	)	)	PUNCT
ejpam-393	96	28	.	.	PUNCT
ejpam-393	97	1	an	an	DET
ejpam-393	97	2	sc	sc	PROPN
ejpam-393	97	3	word	word	NOUN
ejpam-393	97	4	is	be	AUX
ejpam-393	97	5	a	a	DET
ejpam-393	97	6	finite	finite	ADJ
ejpam-393	97	7	string	string	NOUN
ejpam-393	97	8	of	of	ADP
ejpam-393	97	9	substitutions	substitution	NOUN
ejpam-393	97	10	and	and	CCONJ
ejpam-393	97	11	cylindrifications	cylindrification	NOUN
ejpam-393	97	12	any	any	DET
ejpam-393	97	13	sc	sc	PROPN
ejpam-393	97	14	word	word	NOUN
ejpam-393	97	15	w	w	NOUN
ejpam-393	97	16	induces	induce	VERB
ejpam-393	97	17	a	a	DET
ejpam-393	97	18	partial	partial	ADJ
ejpam-393	97	19	map	map	NOUN
ejpam-393	97	20	ŵ	ŵ	X
ejpam-393	97	21	:	:	PUNCT
ejpam-393	97	22	n→	n→	X
ejpam-393	97	23	n	n	CCONJ
ejpam-393	97	24	by	by	ADP
ejpam-393	97	25	•	•	NUM
ejpam-393	97	26	ε̂	ε̂	X
ejpam-393	98	1	=	=	PUNCT
ejpam-393	98	2	i	i	PROPN
ejpam-393	98	3	d	d	PROPN
ejpam-393	98	4	•	•	NUM
ejpam-393	99	1	cw	cw	VERB
ejpam-393	99	2	i	i	PRON
ejpam-393	99	3	j	j	PROPN
ejpam-393	99	4	=	=	X
ejpam-393	99	5	ŵ	ŵ	PUNCT
ejpam-393	99	6	◦	◦	NOUN
ejpam-393	100	1	[	[	X
ejpam-393	100	2	i|	i|	PROPN
ejpam-393	100	3	j	j	PROPN
ejpam-393	100	4	]	]	X
ejpam-393	100	5	•	•	NUM
ejpam-393	100	6	dwci	dwci	NOUN
ejpam-393	100	7	=	=	SYM
ejpam-393	100	8	ŵ	ŵ	X
ejpam-393	100	9	↾	↾	X
ejpam-393	100	10	(	(	PUNCT
ejpam-393	100	11	n∼	n∼	NOUN
ejpam-393	100	12	{	{	PUNCT
ejpam-393	100	13	i	i	NOUN
ejpam-393	100	14	}	}	PUNCT
ejpam-393	100	15	t.	t.	PROPN
ejpam-393	100	16	ahmed	ahmed	PROPN
ejpam-393	100	17	/	/	SYM
ejpam-393	100	18	eur	eur	PROPN
ejpam-393	100	19	.	.	PUNCT
ejpam-393	101	1	j.	j.	PROPN
ejpam-393	101	2	pure	pure	PROPN
ejpam-393	101	3	appl	appl	PROPN
ejpam-393	101	4	.	.	PROPN
ejpam-393	101	5	math	math	PROPN
ejpam-393	101	6	,	,	PUNCT
ejpam-393	101	7	3	3	NUM
ejpam-393	101	8	(	(	PUNCT
ejpam-393	101	9	2010	2010	NUM
ejpam-393	101	10	)	)	PUNCT
ejpam-393	101	11	,	,	PUNCT
ejpam-393	101	12	853	853	NUM
ejpam-393	101	13	-	-	SYM
ejpam-393	101	14	880	880	NUM
ejpam-393	101	15	856	856	NUM
ejpam-393	101	16	if	if	SCONJ
ejpam-393	101	17	ā	ā	ADJ
ejpam-393	101	18	∈	∈	PROPN
ejpam-393	101	19	<	<	X
ejpam-393	101	20	n−1n	n−1n	NOUN
ejpam-393	101	21	,	,	PUNCT
ejpam-393	101	22	we	we	PRON
ejpam-393	101	23	write	write	VERB
ejpam-393	101	24	sā	sā	PROPN
ejpam-393	101	25	,	,	PUNCT
ejpam-393	101	26	or	or	CCONJ
ejpam-393	101	27	more	more	ADV
ejpam-393	101	28	frequently	frequently	ADV
ejpam-393	101	29	sa0	sa0	NOUN
ejpam-393	101	30	...	...	PUNCT
ejpam-393	101	31	ak−1	ak−1	ADJ
ejpam-393	101	32	,	,	PUNCT
ejpam-393	101	33	where	where	SCONJ
ejpam-393	101	34	k	k	PROPN
ejpam-393	101	35	=	=	SYM
ejpam-393	101	36	|ā|	|ā|	PROPN
ejpam-393	101	37	,	,	PUNCT
ejpam-393	101	38	for	for	ADP
ejpam-393	101	39	an	an	DET
ejpam-393	101	40	an	an	DET
ejpam-393	101	41	arbitrary	arbitrary	ADJ
ejpam-393	101	42	chosen	choose	VERB
ejpam-393	101	43	sc	sc	PROPN
ejpam-393	101	44	word	word	NOUN
ejpam-393	101	45	w	w	ADP
ejpam-393	101	46	such	such	ADJ
ejpam-393	101	47	that	that	DET
ejpam-393	101	48	ŵ	ŵ	PROPN
ejpam-393	101	49	=	=	PUNCT
ejpam-393	101	50	ā.	ā.	PROPN
ejpam-393	101	51	w	w	NOUN
ejpam-393	101	52	exists	exist	NOUN
ejpam-393	101	53	and	and	CCONJ
ejpam-393	101	54	does	do	AUX
ejpam-393	101	55	not	not	PART
ejpam-393	101	56	depend	depend	VERB
ejpam-393	101	57	on	on	ADP
ejpam-393	101	58	w	w	NOUN
ejpam-393	101	59	by	by	ADP
ejpam-393	101	60	[	[	X
ejpam-393	101	61	9	9	NUM
ejpam-393	101	62	,	,	PUNCT
ejpam-393	101	63	definition	definition	NOUN
ejpam-393	101	64	5.23	5.23	NUM
ejpam-393	101	65	lemma	lemma	PROPN
ejpam-393	101	66	13.29	13.29	NUM
ejpam-393	101	67	]	]	PUNCT
ejpam-393	101	68	.	.	PUNCT
ejpam-393	102	1	we	we	PRON
ejpam-393	102	2	can	can	AUX
ejpam-393	102	3	,	,	PUNCT
ejpam-393	102	4	and	and	CCONJ
ejpam-393	102	5	will	will	AUX
ejpam-393	102	6	assume	assume	VERB
ejpam-393	102	7	[	[	X
ejpam-393	102	8	9	9	NUM
ejpam-393	102	9	,	,	PUNCT
ejpam-393	102	10	lemma	lemma	PROPN
ejpam-393	102	11	13.29	13.29	NUM
ejpam-393	102	12	]	]	PUNCT
ejpam-393	102	13	that	that	DET
ejpam-393	102	14	w	w	PROPN
ejpam-393	102	15	=	=	PUNCT
ejpam-393	102	16	scn−1cn	scn−1cn	PROPN
ejpam-393	102	17	.	.	PUNCT
ejpam-393	103	1	[	[	X
ejpam-393	103	2	in	in	ADP
ejpam-393	103	3	the	the	DET
ejpam-393	103	4	notation	notation	NOUN
ejpam-393	103	5	of	of	ADP
ejpam-393	103	6	[	[	X
ejpam-393	103	7	9	9	NUM
ejpam-393	103	8	,	,	PUNCT
ejpam-393	103	9	definition	definition	NOUN
ejpam-393	103	10	5.23	5.23	NUM
ejpam-393	103	11	,	,	PUNCT
ejpam-393	103	12	lemma	lemma	PROPN
ejpam-393	103	13	13.29	13.29	NUM
ejpam-393	103	14	]	]	PUNCT
ejpam-393	103	15	,	,	PUNCT
ejpam-393	103	16	ósi	ósi	PROPN
ejpam-393	103	17	jk	jk	PROPN
ejpam-393	103	18	for	for	ADP
ejpam-393	103	19	example	example	NOUN
ejpam-393	103	20	is	be	AUX
ejpam-393	103	21	the	the	DET
ejpam-393	103	22	function	function	NOUN
ejpam-393	103	23	n	n	NOUN
ejpam-393	103	24	→	→	SYM
ejpam-393	103	25	n	n	CCONJ
ejpam-393	103	26	taking	take	VERB
ejpam-393	103	27	0	0	NUM
ejpam-393	103	28	to	to	ADP
ejpam-393	103	29	i	i	PRON
ejpam-393	103	30	,	,	PUNCT
ejpam-393	103	31	1	1	NUM
ejpam-393	103	32	to	to	ADP
ejpam-393	103	33	j	j	PROPN
ejpam-393	103	34	and	and	CCONJ
ejpam-393	103	35	2	2	NUM
ejpam-393	103	36	to	to	ADP
ejpam-393	103	37	k	k	NOUN
ejpam-393	103	38	,	,	PUNCT
ejpam-393	103	39	and	and	CCONJ
ejpam-393	103	40	fixing	fix	VERB
ejpam-393	103	41	all	all	DET
ejpam-393	103	42	l	l	NOUN
ejpam-393	103	43	∈	∈	NOUN
ejpam-393	103	44	n	n	PRON
ejpam-393	103	45	\	\	NOUN
ejpam-393	103	46	{	{	PUNCT
ejpam-393	103	47	i	i	PROPN
ejpam-393	103	48	,	,	PUNCT
ejpam-393	103	49	j	j	PROPN
ejpam-393	103	50	,	,	PUNCT
ejpam-393	103	51	k	k	NOUN
ejpam-393	103	52	}	}	PUNCT
ejpam-393	103	53	.	.	PUNCT
ejpam-393	103	54	]	]	PUNCT
ejpam-393	104	1	let	let	VERB
ejpam-393	104	2	δ	δ	PRON
ejpam-393	104	3	be	be	AUX
ejpam-393	104	4	a	a	DET
ejpam-393	104	5	map	map	NOUN
ejpam-393	104	6	.	.	PUNCT
ejpam-393	105	1	then	then	ADV
ejpam-393	105	2	δ[i	δ[i	NUM
ejpam-393	105	3	→	→	SYM
ejpam-393	105	4	d	d	X
ejpam-393	105	5	]	]	X
ejpam-393	105	6	is	be	AUX
ejpam-393	105	7	defined	define	VERB
ejpam-393	105	8	as	as	SCONJ
ejpam-393	105	9	follows	follow	VERB
ejpam-393	105	10	.	.	PUNCT
ejpam-393	106	1	δ[i→	δ[i→	X
ejpam-393	106	2	d](x	d](x	X
ejpam-393	106	3	)	)	PUNCT
ejpam-393	107	1	=	=	SYM
ejpam-393	107	2	δ(x	δ(x	NOUN
ejpam-393	107	3	)	)	PUNCT
ejpam-393	107	4	if	if	SCONJ
ejpam-393	107	5	x	x	PROPN
ejpam-393	107	6	6=	6=	NOUN
ejpam-393	107	7	i	i	PRON
ejpam-393	107	8	and	and	CCONJ
ejpam-393	107	9	δ[i→	δ[i→	NOUN
ejpam-393	107	10	d](i	d](i	NOUN
ejpam-393	107	11	)	)	PUNCT
ejpam-393	108	1	=	=	SYM
ejpam-393	109	1	d	d	X
ejpam-393	109	2	.	.	PUNCT
ejpam-393	110	1	we	we	PRON
ejpam-393	110	2	write	write	VERB
ejpam-393	110	3	δ	δ	PROPN
ejpam-393	110	4	j	j	PROPN
ejpam-393	110	5	i	i	PRON
ejpam-393	110	6	for	for	ADP
ejpam-393	110	7	δ[i→	δ[i→	PROPN
ejpam-393	110	8	δ	δ	PROPN
ejpam-393	110	9	j	j	PROPN
ejpam-393	110	10	]	]	PUNCT
ejpam-393	110	11	.	.	PUNCT
ejpam-393	111	1	definition	definition	NOUN
ejpam-393	111	2	2	2	NUM
ejpam-393	111	3	.	.	PUNCT
ejpam-393	111	4	from	from	ADP
ejpam-393	111	5	now	now	ADV
ejpam-393	111	6	on	on	ADV
ejpam-393	111	7	let	let	VERB
ejpam-393	111	8	2	2	NUM
ejpam-393	111	9	≤	≤	NOUN
ejpam-393	111	10	n	n	PRON
ejpam-393	111	11	<	<	X
ejpam-393	111	12	ω	ω	NUM
ejpam-393	111	13	.	.	PUNCT
ejpam-393	112	1	let	let	VERB
ejpam-393	112	2	c	c	PRON
ejpam-393	112	3	be	be	AUX
ejpam-393	112	4	an	an	DET
ejpam-393	112	5	atomic	atomic	ADJ
ejpam-393	112	6	can	can	NOUN
ejpam-393	112	7	.	.	PUNCT
ejpam-393	113	1	an	an	DET
ejpam-393	113	2	atomic	atomic	ADJ
ejpam-393	113	3	network	network	NOUN
ejpam-393	113	4	over	over	ADP
ejpam-393	113	5	c	c	PROPN
ejpam-393	113	6	is	be	AUX
ejpam-393	113	7	a	a	DET
ejpam-393	113	8	map	map	NOUN
ejpam-393	113	9	n	n	NOUN
ejpam-393	113	10	:	:	PUNCT
ejpam-393	113	11	n∆→	n∆→	X
ejpam-393	113	12	atc	atc	NOUN
ejpam-393	113	13	such	such	ADJ
ejpam-393	113	14	that	that	SCONJ
ejpam-393	113	15	the	the	DET
ejpam-393	113	16	following	follow	VERB
ejpam-393	113	17	hold	hold	NOUN
ejpam-393	113	18	for	for	ADP
ejpam-393	113	19	each	each	DET
ejpam-393	113	20	i	i	PRON
ejpam-393	113	21	,	,	PUNCT
ejpam-393	113	22	j	j	PROPN
ejpam-393	113	23	<	<	X
ejpam-393	113	24	n	n	PROPN
ejpam-393	113	25	,	,	PUNCT
ejpam-393	113	26	δ	δ	PROPN
ejpam-393	113	27	∈	∈	PROPN
ejpam-393	113	28	n∆	n∆	NOUN
ejpam-393	113	29	and	and	CCONJ
ejpam-393	113	30	d	d	ADP
ejpam-393	113	31	∈∆	∈∆	NOUN
ejpam-393	113	32	:	:	PUNCT
ejpam-393	113	33	•	•	NUM
ejpam-393	113	34	n(δi	n(δi	NUM
ejpam-393	113	35	j	j	NOUN
ejpam-393	113	36	)	)	PUNCT
ejpam-393	113	37	≤	≤	PROPN
ejpam-393	113	38	di	di	X
ejpam-393	113	39	j	j	PROPN
ejpam-393	113	40	•	•	NUM
ejpam-393	113	41	n(δ[i→	n(δ[i→	PROPN
ejpam-393	113	42	d])≤	d])≤	PROPN
ejpam-393	113	43	cin(δ	cin(δ	PROPN
ejpam-393	113	44	)	)	PUNCT
ejpam-393	113	45	note	note	NOUN
ejpam-393	113	46	than	than	SCONJ
ejpam-393	113	47	n	n	PRON
ejpam-393	113	48	can	can	AUX
ejpam-393	113	49	be	be	AUX
ejpam-393	113	50	viewed	view	VERB
ejpam-393	113	51	as	as	ADP
ejpam-393	113	52	a	a	DET
ejpam-393	113	53	hypergraph	hypergraph	NOUN
ejpam-393	113	54	with	with	ADP
ejpam-393	113	55	set	set	NOUN
ejpam-393	113	56	of	of	ADP
ejpam-393	113	57	nodes	node	NOUN
ejpam-393	113	58	∆	∆	PROPN
ejpam-393	113	59	and	and	CCONJ
ejpam-393	113	60	each	each	DET
ejpam-393	113	61	hyperedge	hyperedge	NOUN
ejpam-393	113	62	in	in	ADP
ejpam-393	113	63	µ∆	µ∆	NOUN
ejpam-393	113	64	is	be	AUX
ejpam-393	113	65	labeled	label	VERB
ejpam-393	113	66	with	with	ADP
ejpam-393	113	67	an	an	DET
ejpam-393	113	68	atom	atom	NOUN
ejpam-393	113	69	from	from	ADP
ejpam-393	113	70	c.	c.	PROPN
ejpam-393	113	71	we	we	PRON
ejpam-393	113	72	call	call	VERB
ejpam-393	113	73	such	such	ADJ
ejpam-393	113	74	hyperedges	hyperedge	NOUN
ejpam-393	113	75	atomic	atomic	ADJ
ejpam-393	113	76	hyperedges	hyperedge	NOUN
ejpam-393	113	77	.	.	PUNCT
ejpam-393	114	1	we	we	PRON
ejpam-393	114	2	write	write	VERB
ejpam-393	114	3	nodes(n	nodes(n	PROPN
ejpam-393	114	4	)	)	PUNCT
ejpam-393	114	5	for	for	ADP
ejpam-393	114	6	∆.	∆.	PROPN
ejpam-393	114	7	but	but	CCONJ
ejpam-393	114	8	it	it	PRON
ejpam-393	114	9	can	can	AUX
ejpam-393	114	10	happen	happen	VERB
ejpam-393	114	11	let	let	VERB
ejpam-393	114	12	n	n	PRON
ejpam-393	114	13	stand	stand	VERB
ejpam-393	114	14	for	for	ADP
ejpam-393	114	15	the	the	DET
ejpam-393	114	16	set	set	NOUN
ejpam-393	114	17	of	of	ADP
ejpam-393	114	18	nodes	node	NOUN
ejpam-393	114	19	as	as	ADV
ejpam-393	114	20	well	well	ADV
ejpam-393	114	21	as	as	ADP
ejpam-393	114	22	for	for	ADP
ejpam-393	114	23	the	the	DET
ejpam-393	114	24	function	function	NOUN
ejpam-393	114	25	and	and	CCONJ
ejpam-393	114	26	the	the	DET
ejpam-393	114	27	network	network	NOUN
ejpam-393	114	28	itself	itself	PRON
ejpam-393	114	29	.	.	PUNCT
ejpam-393	115	1	context	context	NOUN
ejpam-393	115	2	will	will	AUX
ejpam-393	115	3	help	help	VERB
ejpam-393	115	4	.	.	PUNCT
ejpam-393	116	1	define	define	VERB
ejpam-393	116	2	x	x	PUNCT
ejpam-393	116	3	∼	∼	NOUN
ejpam-393	116	4	y	y	NOUN
ejpam-393	116	5	if	if	SCONJ
ejpam-393	116	6	there	there	PRON
ejpam-393	116	7	exists	exist	VERB
ejpam-393	116	8	z̄	z̄	INTJ
ejpam-393	116	9	such	such	ADJ
ejpam-393	116	10	that	that	SCONJ
ejpam-393	116	11	n(x	n(x	PROPN
ejpam-393	116	12	,	,	PUNCT
ejpam-393	116	13	y	y	PROPN
ejpam-393	116	14	,	,	PUNCT
ejpam-393	116	15	z̄	z̄	NOUN
ejpam-393	116	16	)	)	PUNCT
ejpam-393	116	17	≤	≤	NOUN
ejpam-393	116	18	d01	d01	NOUN
ejpam-393	116	19	.	.	PUNCT
ejpam-393	117	1	define	define	VERB
ejpam-393	117	2	an	an	DET
ejpam-393	117	3	equivalence	equivalence	NOUN
ejpam-393	117	4	relation	relation	NOUN
ejpam-393	117	5	∼	∼	NOUN
ejpam-393	117	6	over	over	ADP
ejpam-393	117	7	the	the	DET
ejpam-393	117	8	set	set	NOUN
ejpam-393	117	9	of	of	ADP
ejpam-393	117	10	all	all	DET
ejpam-393	117	11	finite	finite	ADJ
ejpam-393	117	12	sequences	sequence	NOUN
ejpam-393	117	13	over	over	ADP
ejpam-393	117	14	nodes(n	nodes(n	NOUN
ejpam-393	117	15	)	)	PUNCT
ejpam-393	117	16	by	by	ADP
ejpam-393	117	17	x̄	x̄	PRON
ejpam-393	117	18	∼	∼	PROPN
ejpam-393	117	19	ȳ	ȳ	PROPN
ejpam-393	117	20	iff	iff	NOUN
ejpam-393	117	21	|	|	ADV
ejpam-393	117	22	x̄	x̄	NUM
ejpam-393	118	1	|	|	ADV
ejpam-393	118	2	=	=	SYM
ejpam-393	119	1	|	|	ADV
ejpam-393	119	2	ȳ	ȳ	NOUN
ejpam-393	120	1	|	|	ADV
ejpam-393	121	1	and	and	CCONJ
ejpam-393	121	2	x	x	AUX
ejpam-393	121	3	i	i	PRON
ejpam-393	121	4	∼	∼	VERB
ejpam-393	121	5	yi	yi	NOUN
ejpam-393	121	6	for	for	ADP
ejpam-393	121	7	all	all	PRON
ejpam-393	121	8	i	i	PRON
ejpam-393	121	9	<	<	X
ejpam-393	122	1	|	|	ADV
ejpam-393	122	2	x̄	x̄	NUM
ejpam-393	122	3	|	|	NOUN
ejpam-393	122	4	.	.	PUNCT
ejpam-393	123	1	(	(	PUNCT
ejpam-393	123	2	3	3	X
ejpam-393	123	3	)	)	PUNCT
ejpam-393	123	4	a	a	DET
ejpam-393	123	5	hypernetwork	hypernetwork	NOUN
ejpam-393	123	6	n	n	NOUN
ejpam-393	123	7	=	=	SYM
ejpam-393	123	8	(	(	PUNCT
ejpam-393	123	9	n	n	CCONJ
ejpam-393	123	10	a	a	PROPN
ejpam-393	123	11	,	,	PUNCT
ejpam-393	123	12	nh	nh	PROPN
ejpam-393	123	13	)	)	PUNCT
ejpam-393	123	14	over	over	ADP
ejpam-393	123	15	c	c	NOUN
ejpam-393	123	16	consists	consist	VERB
ejpam-393	123	17	of	of	ADP
ejpam-393	123	18	a	a	DET
ejpam-393	123	19	network	network	NOUN
ejpam-393	123	20	n	n	CCONJ
ejpam-393	123	21	a	a	DET
ejpam-393	123	22	together	together	NOUN
ejpam-393	123	23	with	with	ADP
ejpam-393	123	24	a	a	DET
ejpam-393	123	25	labelling	labelling	NOUN
ejpam-393	123	26	function	function	NOUN
ejpam-393	123	27	for	for	ADP
ejpam-393	123	28	hyperlabels	hyperlabels	PROPN
ejpam-393	123	29	nh	nh	PROPN
ejpam-393	123	30	:	:	PUNCT
ejpam-393	123	31	<	<	X
ejpam-393	123	32	ωnodes(n)→	ωnodes(n)→	PROPN
ejpam-393	123	33	λ	λ	PROPN
ejpam-393	123	34	(	(	PUNCT
ejpam-393	123	35	some	some	DET
ejpam-393	123	36	arbitrary	arbitrary	ADJ
ejpam-393	123	37	set	set	NOUN
ejpam-393	123	38	of	of	ADP
ejpam-393	123	39	hyperlabels	hyperlabels	PROPN
ejpam-393	123	40	λ	λ	NOUN
ejpam-393	123	41	)	)	PUNCT
ejpam-393	123	42	such	such	ADJ
ejpam-393	123	43	that	that	PRON
ejpam-393	123	44	for	for	ADP
ejpam-393	123	45	x̄	x̄	NOUN
ejpam-393	123	46	,	,	PUNCT
ejpam-393	123	47	ȳ	ȳ	PROPN
ejpam-393	123	48	∈	∈	PROPN
ejpam-393	123	49	<	<	X
ejpam-393	123	50	ωnodes(n	ωnodes(n	NOUN
ejpam-393	123	51	)	)	PUNCT
ejpam-393	123	52	iv	iv	NUM
ejpam-393	123	53	.	.	PUNCT
ejpam-393	124	1	x̄	x̄	NOUN
ejpam-393	124	2	∼	∼	VERB
ejpam-393	124	3	ȳ	ȳ	PROPN
ejpam-393	124	4	⇒	⇒	PROPN
ejpam-393	124	5	nh	nh	PROPN
ejpam-393	124	6	(	(	PUNCT
ejpam-393	124	7	x̄	x̄	PROPN
ejpam-393	124	8	)	)	PUNCT
ejpam-393	124	9	=	=	SYM
ejpam-393	124	10	nh	nh	PROPN
ejpam-393	124	11	(	(	PUNCT
ejpam-393	124	12	ȳ	ȳ	PROPN
ejpam-393	124	13	)	)	PUNCT
ejpam-393	124	14	.	.	PUNCT
ejpam-393	125	1	if	if	SCONJ
ejpam-393	125	2	|	|	ADV
ejpam-393	125	3	x̄|	x̄|	NOUN
ejpam-393	125	4	=	=	PUNCT
ejpam-393	125	5	k	k	PROPN
ejpam-393	125	6	∈	∈	PROPN
ejpam-393	125	7	nats	nat	NOUN
ejpam-393	125	8	and	and	CCONJ
ejpam-393	125	9	nh	nh	PROPN
ejpam-393	125	10	(	(	PUNCT
ejpam-393	125	11	x̄	x̄	PROPN
ejpam-393	125	12	)	)	PUNCT
ejpam-393	126	1	=	=	PUNCT
ejpam-393	126	2	λ	λ	NOUN
ejpam-393	126	3	then	then	ADV
ejpam-393	126	4	we	we	PRON
ejpam-393	126	5	say	say	VERB
ejpam-393	126	6	that	that	SCONJ
ejpam-393	126	7	λ	λ	PROPN
ejpam-393	126	8	is	be	AUX
ejpam-393	126	9	a	a	DET
ejpam-393	126	10	k	k	ADJ
ejpam-393	126	11	-	-	ADJ
ejpam-393	126	12	ary	ary	PROPN
ejpam-393	126	13	hyperlabel	hyperlabel	PROPN
ejpam-393	126	14	.	.	PUNCT
ejpam-393	127	1	(	(	PUNCT
ejpam-393	127	2	x̄	x̄	X
ejpam-393	127	3	)	)	PUNCT
ejpam-393	127	4	is	be	AUX
ejpam-393	127	5	referred	refer	VERB
ejpam-393	127	6	to	to	ADP
ejpam-393	127	7	a	a	DET
ejpam-393	127	8	a	a	DET
ejpam-393	127	9	k	k	ADJ
ejpam-393	127	10	-	-	ADJ
ejpam-393	127	11	ary	ary	ADJ
ejpam-393	127	12	hyperedge	hyperedge	NOUN
ejpam-393	127	13	,	,	PUNCT
ejpam-393	127	14	or	or	CCONJ
ejpam-393	127	15	simply	simply	ADV
ejpam-393	127	16	a	a	DET
ejpam-393	127	17	hyperedge	hyperedge	NOUN
ejpam-393	127	18	.	.	PUNCT
ejpam-393	128	1	(	(	PUNCT
ejpam-393	128	2	note	note	VERB
ejpam-393	128	3	that	that	SCONJ
ejpam-393	128	4	we	we	PRON
ejpam-393	128	5	have	have	VERB
ejpam-393	128	6	atomic	atomic	ADJ
ejpam-393	128	7	hyperedges	hyperedge	NOUN
ejpam-393	128	8	and	and	CCONJ
ejpam-393	128	9	hyperedges	hyperedge	NOUN
ejpam-393	128	10	)	)	PUNCT
ejpam-393	128	11	when	when	SCONJ
ejpam-393	128	12	there	there	PRON
ejpam-393	128	13	is	be	VERB
ejpam-393	128	14	no	no	DET
ejpam-393	128	15	risk	risk	NOUN
ejpam-393	128	16	of	of	ADP
ejpam-393	128	17	ambiguity	ambiguity	NOUN
ejpam-393	128	18	we	we	PRON
ejpam-393	128	19	may	may	AUX
ejpam-393	128	20	drop	drop	VERB
ejpam-393	128	21	the	the	DET
ejpam-393	128	22	superscripts	superscript	NOUN
ejpam-393	128	23	a	a	PRON
ejpam-393	128	24	,	,	PUNCT
ejpam-393	128	25	h.	h.	PROPN
ejpam-393	128	26	the	the	DET
ejpam-393	128	27	following	follow	VERB
ejpam-393	128	28	notation	notation	NOUN
ejpam-393	128	29	is	be	AUX
ejpam-393	128	30	defined	define	VERB
ejpam-393	128	31	for	for	ADP
ejpam-393	128	32	hypernetworks	hypernetwork	NOUN
ejpam-393	128	33	,	,	PUNCT
ejpam-393	128	34	but	but	CCONJ
ejpam-393	128	35	applies	apply	VERB
ejpam-393	128	36	equally	equally	ADV
ejpam-393	128	37	to	to	ADP
ejpam-393	128	38	networks	network	NOUN
ejpam-393	128	39	.	.	PUNCT
ejpam-393	129	1	(	(	PUNCT
ejpam-393	129	2	4	4	X
ejpam-393	129	3	)	)	PUNCT
ejpam-393	129	4	if	if	SCONJ
ejpam-393	129	5	n	n	PRON
ejpam-393	129	6	is	be	AUX
ejpam-393	129	7	a	a	DET
ejpam-393	129	8	hypernetwork	hypernetwork	NOUN
ejpam-393	129	9	and	and	CCONJ
ejpam-393	129	10	s	s	NOUN
ejpam-393	129	11	is	be	AUX
ejpam-393	129	12	any	any	DET
ejpam-393	129	13	set	set	NOUN
ejpam-393	129	14	then	then	ADV
ejpam-393	129	15	n	n	CCONJ
ejpam-393	129	16	↾	↾	PRON
ejpam-393	129	17	s	s	PART
ejpam-393	129	18	is	be	AUX
ejpam-393	129	19	the	the	DET
ejpam-393	129	20	n	n	ADV
ejpam-393	129	21	-	-	PUNCT
ejpam-393	129	22	dimensional	dimensional	ADJ
ejpam-393	129	23	hypernetwork	hypernetwork	NOUN
ejpam-393	129	24	defined	define	VERB
ejpam-393	129	25	by	by	ADP
ejpam-393	129	26	restricting	restrict	VERB
ejpam-393	129	27	n	n	NOUN
ejpam-393	129	28	to	to	ADP
ejpam-393	129	29	the	the	DET
ejpam-393	129	30	set	set	NOUN
ejpam-393	129	31	of	of	ADP
ejpam-393	129	32	nodes	node	NOUN
ejpam-393	129	33	s	s	PART
ejpam-393	129	34	∩	∩	NOUN
ejpam-393	129	35	nodes(n	nodes(n	NOUN
ejpam-393	129	36	)	)	PUNCT
ejpam-393	129	37	.	.	PUNCT
ejpam-393	130	1	for	for	ADP
ejpam-393	130	2	hypernetworks	hypernetwork	NOUN
ejpam-393	130	3	m	m	VERB
ejpam-393	130	4	,	,	PUNCT
ejpam-393	130	5	n	n	CCONJ
ejpam-393	130	6	if	if	SCONJ
ejpam-393	130	7	there	there	PRON
ejpam-393	130	8	is	be	VERB
ejpam-393	130	9	a	a	DET
ejpam-393	130	10	set	set	NOUN
ejpam-393	130	11	s	s	PRON
ejpam-393	131	1	such	such	ADJ
ejpam-393	131	2	that	that	SCONJ
ejpam-393	131	3	m	m	PROPN
ejpam-393	131	4	=	=	SYM
ejpam-393	131	5	n	n	CCONJ
ejpam-393	131	6	↾	↾	NOUN
ejpam-393	131	7	s	s	VERB
ejpam-393	131	8	then	then	ADV
ejpam-393	131	9	we	we	PRON
ejpam-393	131	10	write	write	VERB
ejpam-393	131	11	m	m	PROPN
ejpam-393	131	12	⊆	⊆	NUM
ejpam-393	131	13	n	n	NOUN
ejpam-393	131	14	.	.	PUNCT
ejpam-393	132	1	if	if	SCONJ
ejpam-393	132	2	n0	n0	ADJ
ejpam-393	132	3	⊆	⊆	NUM
ejpam-393	132	4	n1	n1	NOUN
ejpam-393	132	5	⊆	⊆	NUM
ejpam-393	132	6	.	.	PUNCT
ejpam-393	132	7	.	.	PUNCT
ejpam-393	132	8	.	.	PUNCT
ejpam-393	132	9	is	be	AUX
ejpam-393	132	10	a	a	DET
ejpam-393	132	11	nested	nested	ADJ
ejpam-393	132	12	sequence	sequence	NOUN
ejpam-393	132	13	of	of	ADP
ejpam-393	132	14	hypernetworks	hypernetwork	NOUN
ejpam-393	132	15	then	then	ADV
ejpam-393	132	16	we	we	PRON
ejpam-393	132	17	let	let	VERB
ejpam-393	132	18	the	the	DET
ejpam-393	132	19	limit	limit	NOUN
ejpam-393	132	20	n	n	NOUN
ejpam-393	132	21	=	=	PUNCT
ejpam-393	132	22	⋃	⋃	PROPN
ejpam-393	133	1	i	i	PRON
ejpam-393	133	2	<	<	PROPN
ejpam-393	133	3	ω	ω	PROPN
ejpam-393	133	4	ni	ni	PROPN
ejpam-393	133	5	be	be	AUX
ejpam-393	133	6	the	the	DET
ejpam-393	133	7	hypernetwork	hypernetwork	NOUN
ejpam-393	133	8	defined	define	VERB
ejpam-393	133	9	by	by	ADP
ejpam-393	133	10	nodes(n	nodes(n	NOUN
ejpam-393	133	11	)	)	PUNCT
ejpam-393	134	1	=	=	NOUN
ejpam-393	134	2	⋃	⋃	PROPN
ejpam-393	134	3	i	i	PRON
ejpam-393	134	4	<	<	X
ejpam-393	134	5	ω	ω	X
ejpam-393	134	6	nodes(ni	nodes(ni	PROPN
ejpam-393	134	7	)	)	PUNCT
ejpam-393	134	8	,	,	PUNCT
ejpam-393	134	9	n	n	PRON
ejpam-393	134	10	a(x0	a(x0	VERB
ejpam-393	134	11	,	,	PUNCT
ejpam-393	134	12	.	.	PUNCT
ejpam-393	134	13	.	.	PUNCT
ejpam-393	134	14	.	.	PUNCT
ejpam-393	135	1	xn−1	xn−1	PROPN
ejpam-393	135	2	)	)	PUNCT
ejpam-393	136	1	=	=	SYM
ejpam-393	137	1	n	n	PRON
ejpam-393	137	2	a	a	DET
ejpam-393	137	3	i	i	PRON
ejpam-393	137	4	(	(	PUNCT
ejpam-393	137	5	x0	x0	PROPN
ejpam-393	137	6	,	,	PUNCT
ejpam-393	137	7	.	.	PUNCT
ejpam-393	137	8	.	.	PUNCT
ejpam-393	137	9	.	.	PUNCT
ejpam-393	138	1	xn−1	xn−1	PROPN
ejpam-393	138	2	)	)	PUNCT
ejpam-393	139	1	if	if	SCONJ
ejpam-393	139	2	x0	x0	PROPN
ejpam-393	139	3	.	.	PUNCT
ejpam-393	139	4	.	.	PUNCT
ejpam-393	139	5	.	.	PUNCT
ejpam-393	140	1	xµ−1	xµ−1	PROPN
ejpam-393	140	2	∈	∈	PROPN
ejpam-393	140	3	nodes(ni	nodes(ni	PROPN
ejpam-393	140	4	)	)	PUNCT
ejpam-393	140	5	,	,	PUNCT
ejpam-393	140	6	and	and	CCONJ
ejpam-393	140	7	nh	nh	PROPN
ejpam-393	140	8	(	(	PUNCT
ejpam-393	140	9	x̄	x̄	PROPN
ejpam-393	140	10	)	)	PUNCT
ejpam-393	140	11	=	=	SYM
ejpam-393	141	1	nh	nh	INTJ
ejpam-393	142	1	i	i	PRON
ejpam-393	142	2	(	(	PUNCT
ejpam-393	142	3	x̄	x̄	PROPN
ejpam-393	142	4	)	)	PUNCT
ejpam-393	142	5	if	if	SCONJ
ejpam-393	142	6	rng	rng	PROPN
ejpam-393	142	7	(	(	PUNCT
ejpam-393	142	8	x̄	x̄	PROPN
ejpam-393	142	9	)	)	PUNCT
ejpam-393	142	10	⊆	⊆	NUM
ejpam-393	142	11	nodes(ni	nodes(ni	NOUN
ejpam-393	142	12	)	)	PUNCT
ejpam-393	142	13	.	.	PUNCT
ejpam-393	143	1	this	this	PRON
ejpam-393	143	2	is	be	AUX
ejpam-393	143	3	well	well	ADV
ejpam-393	143	4	-	-	PUNCT
ejpam-393	143	5	defined	define	VERB
ejpam-393	143	6	since	since	SCONJ
ejpam-393	143	7	the	the	DET
ejpam-393	143	8	hypernetworks	hypernetwork	NOUN
ejpam-393	143	9	are	be	AUX
ejpam-393	143	10	nested	nest	VERB
ejpam-393	143	11	and	and	CCONJ
ejpam-393	143	12	since	since	SCONJ
ejpam-393	143	13	hyperedges	hyperedge	NOUN
ejpam-393	143	14	x̄	x̄	X
ejpam-393	143	15	∈	∈	PROPN
ejpam-393	143	16	<	<	X
ejpam-393	143	17	ωnodes(n	ωnodes(n	NOUN
ejpam-393	143	18	)	)	PUNCT
ejpam-393	143	19	are	be	AUX
ejpam-393	143	20	only	only	ADV
ejpam-393	143	21	finitely	finitely	ADV
ejpam-393	143	22	long	long	ADJ
ejpam-393	143	23	.	.	PUNCT
ejpam-393	144	1	for	for	ADP
ejpam-393	144	2	hypernetworks	hypernetwork	NOUN
ejpam-393	144	3	m	m	VERB
ejpam-393	144	4	,	,	PUNCT
ejpam-393	144	5	n	n	PROPN
ejpam-393	144	6	and	and	CCONJ
ejpam-393	144	7	any	any	DET
ejpam-393	144	8	set	set	NOUN
ejpam-393	144	9	s	s	PART
ejpam-393	144	10	,	,	PUNCT
ejpam-393	144	11	we	we	PRON
ejpam-393	144	12	write	write	VERB
ejpam-393	144	13	m	m	PRON
ejpam-393	144	14	≡s	≡s	ADJ
ejpam-393	144	15	n	n	CCONJ
ejpam-393	144	16	if	if	SCONJ
ejpam-393	144	17	n	n	CCONJ
ejpam-393	144	18	↾	↾	X
ejpam-393	144	19	s	s	PART
ejpam-393	144	20	=	=	NOUN
ejpam-393	144	21	m	m	NUM
ejpam-393	144	22	↾	↾	X
ejpam-393	144	23	s	s	X
ejpam-393	144	24	.	.	PUNCT
ejpam-393	145	1	for	for	ADP
ejpam-393	145	2	hypernetworks	hypernetwork	NOUN
ejpam-393	145	3	m	m	VERB
ejpam-393	145	4	,	,	PUNCT
ejpam-393	145	5	n	n	CCONJ
ejpam-393	145	6	,	,	PUNCT
ejpam-393	145	7	and	and	CCONJ
ejpam-393	145	8	any	any	DET
ejpam-393	145	9	set	set	NOUN
ejpam-393	145	10	s	s	PART
ejpam-393	145	11	,	,	PUNCT
ejpam-393	145	12	we	we	PRON
ejpam-393	145	13	write	write	VERB
ejpam-393	145	14	m	m	PRON
ejpam-393	145	15	≡s	≡s	ADJ
ejpam-393	145	16	n	n	CCONJ
ejpam-393	145	17	if	if	SCONJ
ejpam-393	145	18	the	the	DET
ejpam-393	145	19	symmetric	symmetric	ADJ
ejpam-393	145	20	difference	difference	NOUN
ejpam-393	145	21	∆(nodes(m),nodes(n))⊆	∆(nodes(m),nodes(n))⊆	NOUN
ejpam-393	145	22	s	s	NOUN
ejpam-393	145	23	and	and	CCONJ
ejpam-393	145	24	m	m	VERB
ejpam-393	145	25	≡(nodes(m)∪nodes(n))\s	≡(nodes(m)∪nodes(n))\s	NOUN
ejpam-393	145	26	n	n	NOUN
ejpam-393	145	27	.	.	PUNCT
ejpam-393	146	1	we	we	PRON
ejpam-393	146	2	write	write	VERB
ejpam-393	146	3	m	m	VERB
ejpam-393	146	4	≡k	≡k	PROPN
ejpam-393	146	5	n	n	PROPN
ejpam-393	146	6	for	for	ADP
ejpam-393	146	7	m	m	NOUN
ejpam-393	146	8	≡{k	≡{k	NOUN
ejpam-393	146	9	}	}	PUNCT
ejpam-393	146	10	n	n	CCONJ
ejpam-393	146	11	.	.	PUNCT
ejpam-393	147	1	let	let	VERB
ejpam-393	147	2	n	n	PRON
ejpam-393	147	3	be	be	AUX
ejpam-393	147	4	a	a	DET
ejpam-393	147	5	network	network	NOUN
ejpam-393	147	6	and	and	CCONJ
ejpam-393	147	7	let	let	VERB
ejpam-393	147	8	θ	θ	NOUN
ejpam-393	147	9	be	be	AUX
ejpam-393	147	10	any	any	DET
ejpam-393	147	11	function	function	NOUN
ejpam-393	147	12	.	.	PUNCT
ejpam-393	148	1	the	the	DET
ejpam-393	148	2	network	network	NOUN
ejpam-393	148	3	nθ	nθ	NOUN
ejpam-393	148	4	is	be	AUX
ejpam-393	148	5	a	a	DET
ejpam-393	148	6	complete	complete	ADJ
ejpam-393	148	7	labeled	label	VERB
ejpam-393	148	8	graph	graph	NOUN
ejpam-393	148	9	with	with	ADP
ejpam-393	148	10	nodes	node	NOUN
ejpam-393	148	11	θ−1(nodes(n	θ−1(nodes(n	PROPN
ejpam-393	148	12	)	)	PUNCT
ejpam-393	148	13	)	)	PUNCT
ejpam-393	149	1	=	=	PRON
ejpam-393	149	2	{	{	PUNCT
ejpam-393	149	3	x	x	PUNCT
ejpam-393	149	4	∈	∈	NOUN
ejpam-393	149	5	dom(θ	dom(θ	PROPN
ejpam-393	149	6	)	)	PUNCT
ejpam-393	149	7	:	:	PUNCT
ejpam-393	150	1	θ(x	θ(x	PROPN
ejpam-393	150	2	)	)	PUNCT
ejpam-393	150	3	∈	∈	PROPN
ejpam-393	150	4	nodes(n	nodes(n	PROPN
ejpam-393	150	5	)	)	PUNCT
ejpam-393	150	6	}	}	PUNCT
ejpam-393	150	7	,	,	PUNCT
ejpam-393	150	8	and	and	CCONJ
ejpam-393	150	9	labeling	labeling	NOUN
ejpam-393	150	10	defined	define	VERB
ejpam-393	150	11	by	by	ADP
ejpam-393	150	12	t.	t.	PROPN
ejpam-393	150	13	ahmed	ahmed	PROPN
ejpam-393	150	14	/	/	SYM
ejpam-393	150	15	eur	eur	PROPN
ejpam-393	150	16	.	.	PUNCT
ejpam-393	151	1	j.	j.	PROPN
ejpam-393	151	2	pure	pure	PROPN
ejpam-393	151	3	appl	appl	PROPN
ejpam-393	151	4	.	.	PROPN
ejpam-393	151	5	math	math	PROPN
ejpam-393	151	6	,	,	PUNCT
ejpam-393	151	7	3	3	NUM
ejpam-393	151	8	(	(	PUNCT
ejpam-393	151	9	2010	2010	NUM
ejpam-393	151	10	)	)	PUNCT
ejpam-393	151	11	,	,	PUNCT
ejpam-393	151	12	853	853	NUM
ejpam-393	151	13	-	-	SYM
ejpam-393	151	14	880	880	NUM
ejpam-393	151	15	857	857	NUM
ejpam-393	151	16	(	(	PUNCT
ejpam-393	151	17	nθ)(i0	nθ)(i0	NOUN
ejpam-393	151	18	,	,	PUNCT
ejpam-393	151	19	.	.	PUNCT
ejpam-393	151	20	.	.	PUNCT
ejpam-393	151	21	.	.	PUNCT
ejpam-393	152	1	iµ−1	iµ−1	NOUN
ejpam-393	152	2	)	)	PUNCT
ejpam-393	152	3	=	=	PUNCT
ejpam-393	152	4	n(θ(i0),θ(i1),θ(iµ−1	n(θ(i0),θ(i1),θ(iµ−1	NUM
ejpam-393	152	5	)	)	PUNCT
ejpam-393	152	6	)	)	PUNCT
ejpam-393	152	7	,	,	PUNCT
ejpam-393	152	8	for	for	ADP
ejpam-393	152	9	i0	i0	PROPN
ejpam-393	152	10	,	,	PUNCT
ejpam-393	152	11	.	.	PUNCT
ejpam-393	152	12	.	.	PUNCT
ejpam-393	152	13	.	.	PUNCT
ejpam-393	153	1	iµ−1	iµ−1	NOUN
ejpam-393	153	2	∈	∈	PROPN
ejpam-393	153	3	θ	θ	PROPN
ejpam-393	153	4	−1(nodes(n	−1(nodes(n	NUM
ejpam-393	153	5	)	)	PUNCT
ejpam-393	153	6	)	)	PUNCT
ejpam-393	153	7	.	.	PUNCT
ejpam-393	154	1	similarly	similarly	ADV
ejpam-393	154	2	,	,	PUNCT
ejpam-393	154	3	for	for	ADP
ejpam-393	154	4	a	a	DET
ejpam-393	154	5	hypernetwork	hypernetwork	NOUN
ejpam-393	154	6	n	n	NOUN
ejpam-393	154	7	=	=	SYM
ejpam-393	154	8	(	(	PUNCT
ejpam-393	154	9	n	n	X
ejpam-393	154	10	a	a	PROPN
ejpam-393	154	11	,	,	PUNCT
ejpam-393	154	12	nh	nh	PROPN
ejpam-393	154	13	)	)	PUNCT
ejpam-393	154	14	,	,	PUNCT
ejpam-393	154	15	we	we	PRON
ejpam-393	154	16	define	define	VERB
ejpam-393	154	17	nθ	nθ	PART
ejpam-393	154	18	to	to	PART
ejpam-393	154	19	be	be	AUX
ejpam-393	154	20	the	the	DET
ejpam-393	154	21	hypernetwork	hypernetwork	NOUN
ejpam-393	154	22	(	(	PUNCT
ejpam-393	154	23	n	n	CCONJ
ejpam-393	154	24	aθ	aθ	INTJ
ejpam-393	154	25	,	,	PUNCT
ejpam-393	154	26	nhθ	nhθ	NOUN
ejpam-393	154	27	)	)	PUNCT
ejpam-393	154	28	with	with	ADP
ejpam-393	154	29	hyperlabeling	hyperlabele	VERB
ejpam-393	154	30	defined	define	VERB
ejpam-393	154	31	by	by	ADP
ejpam-393	154	32	nhθ(x0	nhθ(x0	ADP
ejpam-393	154	33	,	,	PUNCT
ejpam-393	154	34	x1	x1	PROPN
ejpam-393	154	35	,	,	PUNCT
ejpam-393	154	36	.	.	PUNCT
ejpam-393	154	37	.	.	PUNCT
ejpam-393	154	38	.	.	PUNCT
ejpam-393	154	39	)	)	PUNCT
ejpam-393	155	1	=	=	PUNCT
ejpam-393	155	2	nh(θ(x0),θ(x1	nh(θ(x0),θ(x1	NOUN
ejpam-393	155	3	)	)	PUNCT
ejpam-393	155	4	,	,	PUNCT
ejpam-393	155	5	.	.	PUNCT
ejpam-393	155	6	.	.	PUNCT
ejpam-393	155	7	.	.	PUNCT
ejpam-393	155	8	)	)	PUNCT
ejpam-393	156	1	for	for	ADP
ejpam-393	156	2	(	(	PUNCT
ejpam-393	156	3	x0	x0	PROPN
ejpam-393	156	4	,	,	PUNCT
ejpam-393	156	5	x1	x1	PROPN
ejpam-393	156	6	,	,	PUNCT
ejpam-393	156	7	.	.	PUNCT
ejpam-393	156	8	.	.	PUNCT
ejpam-393	156	9	.	.	PUNCT
ejpam-393	156	10	)	)	PUNCT
ejpam-393	156	11	∈	∈	PROPN
ejpam-393	156	12	<	<	X
ejpam-393	156	13	ωθ−1(nodes(n	ωθ−1(nodes(n	PROPN
ejpam-393	156	14	)	)	PUNCT
ejpam-393	156	15	)	)	PUNCT
ejpam-393	156	16	.	.	PUNCT
ejpam-393	157	1	let	let	VERB
ejpam-393	157	2	m	m	PRON
ejpam-393	157	3	,	,	PUNCT
ejpam-393	157	4	n	n	X
ejpam-393	157	5	be	be	VERB
ejpam-393	157	6	hypernetworks	hypernetwork	NOUN
ejpam-393	157	7	.	.	PUNCT
ejpam-393	158	1	a	a	DET
ejpam-393	158	2	partial	partial	ADJ
ejpam-393	158	3	isomorphism	isomorphism	NOUN
ejpam-393	158	4	θ	θ	NOUN
ejpam-393	158	5	:	:	PUNCT
ejpam-393	158	6	m	m	VERB
ejpam-393	158	7	→	→	SYM
ejpam-393	158	8	n	n	X
ejpam-393	158	9	is	be	AUX
ejpam-393	158	10	a	a	DET
ejpam-393	158	11	partial	partial	ADJ
ejpam-393	158	12	map	map	NOUN
ejpam-393	158	13	θ	θ	NOUN
ejpam-393	158	14	:	:	PUNCT
ejpam-393	158	15	nodes(m)→	nodes(m)→	PRON
ejpam-393	158	16	nodes(n	nodes(n	NOUN
ejpam-393	158	17	)	)	PUNCT
ejpam-393	158	18	such	such	ADJ
ejpam-393	158	19	that	that	PRON
ejpam-393	158	20	for	for	ADP
ejpam-393	158	21	any	any	DET
ejpam-393	158	22	ii	ii	NOUN
ejpam-393	158	23	.	.	PUNCT
ejpam-393	158	24	.	.	PUNCT
ejpam-393	158	25	.	.	PUNCT
ejpam-393	159	1	iµ−1	iµ−1	NOUN
ejpam-393	159	2	∈	∈	PROPN
ejpam-393	159	3	dom(θ)⊆	dom(θ)⊆	PROPN
ejpam-393	159	4	nodes(m	nodes(m	NOUN
ejpam-393	159	5	)	)	PUNCT
ejpam-393	159	6	we	we	PRON
ejpam-393	159	7	have	have	VERB
ejpam-393	159	8	m	m	VERB
ejpam-393	159	9	a(i1	a(i1	ADJ
ejpam-393	159	10	,	,	PUNCT
ejpam-393	159	11	.	.	PUNCT
ejpam-393	159	12	.	.	PUNCT
ejpam-393	159	13	.	.	PUNCT
ejpam-393	160	1	iµ−1	iµ−1	NOUN
ejpam-393	160	2	)	)	PUNCT
ejpam-393	160	3	=	=	SYM
ejpam-393	160	4	n	n	PRON
ejpam-393	160	5	a(θ(i	a(θ(i	VERB
ejpam-393	160	6	)	)	PUNCT
ejpam-393	160	7	,	,	PUNCT
ejpam-393	160	8	.	.	PUNCT
ejpam-393	160	9	.	.	PUNCT
ejpam-393	161	1	.θ(iµ−1	.θ(iµ−1	PUNCT
ejpam-393	161	2	)	)	PUNCT
ejpam-393	161	3	)	)	PUNCT
ejpam-393	162	1	and	and	CCONJ
ejpam-393	162	2	for	for	ADP
ejpam-393	162	3	any	any	DET
ejpam-393	162	4	finite	finite	ADJ
ejpam-393	162	5	sequence	sequence	NOUN
ejpam-393	162	6	x̄	x̄	PRON
ejpam-393	162	7	∈	∈	PROPN
ejpam-393	162	8	<	<	X
ejpam-393	162	9	ωdom(θ	ωdom(θ	X
ejpam-393	162	10	)	)	PUNCT
ejpam-393	162	11	we	we	PRON
ejpam-393	162	12	have	have	AUX
ejpam-393	162	13	mh	mh	PROPN
ejpam-393	162	14	(	(	PUNCT
ejpam-393	162	15	x̄	x̄	PROPN
ejpam-393	162	16	)	)	PUNCT
ejpam-393	162	17	=	=	SYM
ejpam-393	163	1	nhθ	nhθ	PROPN
ejpam-393	163	2	(	(	PUNCT
ejpam-393	163	3	x̄	x̄	PROPN
ejpam-393	163	4	)	)	PUNCT
ejpam-393	163	5	.	.	PUNCT
ejpam-393	164	1	if	if	SCONJ
ejpam-393	164	2	m	m	NOUN
ejpam-393	164	3	=	=	VERB
ejpam-393	164	4	n	n	CCONJ
ejpam-393	164	5	we	we	PRON
ejpam-393	164	6	may	may	AUX
ejpam-393	164	7	call	call	VERB
ejpam-393	164	8	θ	θ	PROPN
ejpam-393	164	9	a	a	DET
ejpam-393	164	10	partial	partial	ADJ
ejpam-393	164	11	isomorphism	isomorphism	NOUN
ejpam-393	164	12	of	of	ADP
ejpam-393	164	13	n	n	PROPN
ejpam-393	164	14	.	.	PUNCT
ejpam-393	165	1	definition	definition	NOUN
ejpam-393	165	2	3	3	NUM
ejpam-393	165	3	.	.	PUNCT
ejpam-393	166	1	let	let	VERB
ejpam-393	166	2	2	2	NUM
ejpam-393	166	3	≤	≤	NOUN
ejpam-393	166	4	n	n	CCONJ
ejpam-393	166	5	<	<	X
ejpam-393	166	6	ω	ω	PROPN
ejpam-393	166	7	.	.	PUNCT
ejpam-393	167	1	for	for	ADP
ejpam-393	167	2	any	any	DET
ejpam-393	167	3	can	can	AUX
ejpam-393	167	4	atom	atom	NOUN
ejpam-393	167	5	structure	structure	NOUN
ejpam-393	167	6	α	α	NOUN
ejpam-393	167	7	,	,	PUNCT
ejpam-393	167	8	and	and	CCONJ
ejpam-393	167	9	n	n	DET
ejpam-393	167	10	≤	≤	NUM
ejpam-393	167	11	m	m	VERB
ejpam-393	167	12	≤	≤	NOUN
ejpam-393	167	13	ω	ω	NUM
ejpam-393	167	14	,	,	PUNCT
ejpam-393	167	15	we	we	PRON
ejpam-393	167	16	define	define	VERB
ejpam-393	167	17	twoplayer	twoplayer	NOUN
ejpam-393	167	18	games	game	NOUN
ejpam-393	167	19	f	f	PROPN
ejpam-393	167	20	m	m	VERB
ejpam-393	167	21	n	n	PROPN
ejpam-393	167	22	(	(	PUNCT
ejpam-393	167	23	α	α	NOUN
ejpam-393	167	24	)	)	PUNCT
ejpam-393	167	25	,	,	PUNCT
ejpam-393	167	26	and	and	CCONJ
ejpam-393	167	27	hn(α	hn(α	NUM
ejpam-393	167	28	)	)	PUNCT
ejpam-393	167	29	,	,	PUNCT
ejpam-393	167	30	each	each	PRON
ejpam-393	167	31	with	with	ADP
ejpam-393	167	32	ω	ω	PROPN
ejpam-393	167	33	rounds	round	NOUN
ejpam-393	167	34	,	,	PUNCT
ejpam-393	167	35	and	and	CCONJ
ejpam-393	167	36	for	for	ADP
ejpam-393	167	37	m	m	PROPN
ejpam-393	167	38	<	<	X
ejpam-393	167	39	ω	ω	X
ejpam-393	167	40	we	we	PRON
ejpam-393	167	41	define	define	VERB
ejpam-393	167	42	hm	hm	INTJ
ejpam-393	167	43	,	,	PUNCT
ejpam-393	167	44	n(α	n(α	PROPN
ejpam-393	167	45	)	)	PUNCT
ejpam-393	167	46	with	with	ADP
ejpam-393	167	47	n	n	ADP
ejpam-393	167	48	rounds	round	NOUN
ejpam-393	167	49	.	.	PUNCT
ejpam-393	168	1	•	•	INTJ
ejpam-393	168	2	let	let	VERB
ejpam-393	168	3	m	m	NOUN
ejpam-393	168	4	≤ω	≤ω	ADJ
ejpam-393	168	5	.	.	PUNCT
ejpam-393	169	1	in	in	ADP
ejpam-393	169	2	a	a	DET
ejpam-393	169	3	play	play	NOUN
ejpam-393	169	4	of	of	ADP
ejpam-393	169	5	f	f	PROPN
ejpam-393	169	6	m	m	VERB
ejpam-393	169	7	n	n	PROPN
ejpam-393	169	8	(	(	PUNCT
ejpam-393	169	9	α	α	X
ejpam-393	169	10	)	)	PUNCT
ejpam-393	169	11	the	the	DET
ejpam-393	169	12	two	two	NUM
ejpam-393	169	13	players	player	NOUN
ejpam-393	169	14	construct	construct	VERB
ejpam-393	169	15	a	a	DET
ejpam-393	169	16	sequence	sequence	NOUN
ejpam-393	169	17	of	of	ADP
ejpam-393	169	18	networks	network	NOUN
ejpam-393	169	19	n0	n0	PROPN
ejpam-393	169	20	,	,	PUNCT
ejpam-393	169	21	n1	n1	NOUN
ejpam-393	169	22	,	,	PUNCT
ejpam-393	169	23	.	.	PUNCT
ejpam-393	169	24	.	.	PUNCT
ejpam-393	170	1	.	.	PUNCT
ejpam-393	171	1	where	where	SCONJ
ejpam-393	171	2	nodes(ni	nodes(ni	NOUN
ejpam-393	171	3	)	)	PUNCT
ejpam-393	171	4	is	be	AUX
ejpam-393	171	5	a	a	DET
ejpam-393	171	6	finite	finite	NOUN
ejpam-393	171	7	subset	subset	NOUN
ejpam-393	171	8	of	of	ADP
ejpam-393	171	9	m=	m=	X
ejpam-393	171	10	{	{	PUNCT
ejpam-393	171	11	j	j	NOUN
ejpam-393	171	12	:	:	PUNCT
ejpam-393	171	13	j	j	PROPN
ejpam-393	171	14	<	<	X
ejpam-393	171	15	m	m	X
ejpam-393	171	16	}	}	PUNCT
ejpam-393	171	17	,	,	PUNCT
ejpam-393	171	18	for	for	ADP
ejpam-393	171	19	each	each	DET
ejpam-393	171	20	i.	i.	NOUN
ejpam-393	171	21	in	in	ADP
ejpam-393	171	22	the	the	DET
ejpam-393	171	23	initial	initial	ADJ
ejpam-393	171	24	round	round	NOUN
ejpam-393	171	25	of	of	ADP
ejpam-393	171	26	this	this	DET
ejpam-393	171	27	game	game	NOUN
ejpam-393	171	28	∀	∀	PUNCT
ejpam-393	171	29	picks	pick	VERB
ejpam-393	171	30	any	any	DET
ejpam-393	171	31	atom	atom	NOUN
ejpam-393	171	32	a	a	DET
ejpam-393	171	33	∈	∈	NOUN
ejpam-393	171	34	α	α	NOUN
ejpam-393	171	35	and	and	CCONJ
ejpam-393	171	36	∃	∃	PROPN
ejpam-393	171	37	must	must	AUX
ejpam-393	171	38	play	play	VERB
ejpam-393	171	39	a	a	DET
ejpam-393	171	40	finite	finite	ADJ
ejpam-393	171	41	network	network	NOUN
ejpam-393	171	42	n0	n0	PROPN
ejpam-393	171	43	with	with	ADP
ejpam-393	171	44	nodes(n0	nodes(n0	NOUN
ejpam-393	171	45	)	)	PUNCT
ejpam-393	171	46	⊆	⊆	NUM
ejpam-393	171	47	n	n	CCONJ
ejpam-393	171	48	,	,	PUNCT
ejpam-393	171	49	such	such	ADJ
ejpam-393	171	50	that	that	SCONJ
ejpam-393	171	51	n0(d̄	n0(d̄	PROPN
ejpam-393	171	52	)	)	PUNCT
ejpam-393	171	53	=	=	PUNCT
ejpam-393	172	1	a	a	PRON
ejpam-393	172	2	for	for	ADP
ejpam-393	172	3	some	some	DET
ejpam-393	172	4	d̄	d̄	PROPN
ejpam-393	172	5	∈	∈	PROPN
ejpam-393	172	6	µnodes(n0	µnodes(n0	NOUN
ejpam-393	172	7	)	)	PUNCT
ejpam-393	172	8	.	.	PUNCT
ejpam-393	173	1	in	in	ADP
ejpam-393	173	2	a	a	DET
ejpam-393	173	3	subsequent	subsequent	ADJ
ejpam-393	173	4	round	round	NOUN
ejpam-393	173	5	of	of	ADP
ejpam-393	173	6	a	a	DET
ejpam-393	173	7	play	play	NOUN
ejpam-393	173	8	of	of	ADP
ejpam-393	173	9	f	f	PROPN
ejpam-393	173	10	m	m	VERB
ejpam-393	173	11	n	n	PROPN
ejpam-393	173	12	(	(	PUNCT
ejpam-393	173	13	α	α	NOUN
ejpam-393	173	14	)	)	PUNCT
ejpam-393	173	15	∀	∀	PUNCT
ejpam-393	173	16	can	can	AUX
ejpam-393	173	17	pick	pick	VERB
ejpam-393	173	18	a	a	DET
ejpam-393	173	19	previously	previously	ADV
ejpam-393	173	20	played	play	VERB
ejpam-393	173	21	network	network	NOUN
ejpam-393	173	22	n	n	CCONJ
ejpam-393	173	23	an	an	DET
ejpam-393	173	24	index	index	NOUN
ejpam-393	173	25	ł	ł	NOUN
ejpam-393	173	26	<	<	X
ejpam-393	173	27	n	n	CCONJ
ejpam-393	173	28	,	,	PUNCT
ejpam-393	173	29	a	a	DET
ejpam-393	173	30	“	"	PUNCT
ejpam-393	173	31	face	face	NOUN
ejpam-393	173	32	”	"	PUNCT
ejpam-393	173	33	f	f	PROPN
ejpam-393	173	34	=	=	PUNCT
ejpam-393	173	35	〈	〈	PROPN
ejpam-393	173	36	f0	f0	PROPN
ejpam-393	173	37	,	,	PUNCT
ejpam-393	173	38	.	.	PUNCT
ejpam-393	173	39	.	.	PUNCT
ejpam-393	173	40	.	.	PUNCT
ejpam-393	174	1	fn−2	fn−2	ADJ
ejpam-393	174	2	〉	〉	NOUN
ejpam-393	174	3	∈	∈	NOUN
ejpam-393	174	4	n−2nodes(n	n−2nodes(n	NOUN
ejpam-393	174	5	)	)	PUNCT
ejpam-393	174	6	,	,	PUNCT
ejpam-393	175	1	k	k	PROPN
ejpam-393	175	2	∈	∈	PROPN
ejpam-393	175	3	m	m	VERB
ejpam-393	175	4	\	\	NOUN
ejpam-393	175	5	{	{	PUNCT
ejpam-393	175	6	f0	f0	PROPN
ejpam-393	175	7	,	,	PUNCT
ejpam-393	175	8	.	.	PUNCT
ejpam-393	175	9	.	.	PUNCT
ejpam-393	175	10	.	.	PUNCT
ejpam-393	176	1	fn−2	fn−2	ADJ
ejpam-393	176	2	}	}	PUNCT
ejpam-393	176	3	,	,	PUNCT
ejpam-393	176	4	and	and	CCONJ
ejpam-393	176	5	an	an	DET
ejpam-393	176	6	atom	atom	NOUN
ejpam-393	176	7	b	b	NOUN
ejpam-393	176	8	∈	∈	NOUN
ejpam-393	176	9	α	α	PRON
ejpam-393	176	10	such	such	ADJ
ejpam-393	176	11	that	that	PRON
ejpam-393	176	12	b	b	PROPN
ejpam-393	176	13	≤	≤	NUM
ejpam-393	176	14	cln	cln	PROPN
ejpam-393	176	15	(	(	PUNCT
ejpam-393	176	16	f0	f0	PROPN
ejpam-393	176	17	,	,	PUNCT
ejpam-393	176	18	.	.	PUNCT
ejpam-393	176	19	.	.	PUNCT
ejpam-393	176	20	.	.	PUNCT
ejpam-393	177	1	fi	fi	INTJ
ejpam-393	177	2	,	,	PUNCT
ejpam-393	177	3	x	x	INTJ
ejpam-393	177	4	,	,	PUNCT
ejpam-393	177	5	.	.	PUNCT
ejpam-393	177	6	.	.	PUNCT
ejpam-393	177	7	.	.	PUNCT
ejpam-393	178	1	fn−2	fn−2	ADJ
ejpam-393	178	2	)	)	PUNCT
ejpam-393	178	3	.	.	PUNCT
ejpam-393	179	1	(	(	PUNCT
ejpam-393	179	2	the	the	DET
ejpam-393	179	3	choice	choice	NOUN
ejpam-393	179	4	of	of	ADP
ejpam-393	179	5	x	x	PUNCT
ejpam-393	179	6	here	here	ADV
ejpam-393	179	7	is	be	AUX
ejpam-393	179	8	arbitrary	arbitrary	ADJ
ejpam-393	179	9	,	,	PUNCT
ejpam-393	179	10	as	as	ADP
ejpam-393	179	11	the	the	DET
ejpam-393	179	12	second	second	ADJ
ejpam-393	179	13	part	part	NOUN
ejpam-393	179	14	of	of	ADP
ejpam-393	179	15	the	the	DET
ejpam-393	179	16	definition	definition	NOUN
ejpam-393	179	17	of	of	ADP
ejpam-393	179	18	an	an	DET
ejpam-393	179	19	atomic	atomic	ADJ
ejpam-393	179	20	network	network	NOUN
ejpam-393	179	21	together	together	ADV
ejpam-393	179	22	with	with	ADP
ejpam-393	179	23	the	the	DET
ejpam-393	179	24	fact	fact	NOUN
ejpam-393	179	25	that	that	SCONJ
ejpam-393	179	26	ci(ci	ci(ci	PROPN
ejpam-393	179	27	x	x	NOUN
ejpam-393	179	28	)	)	PUNCT
ejpam-393	179	29	=	=	SYM
ejpam-393	179	30	ci	ci	NOUN
ejpam-393	179	31	x	x	PUNCT
ejpam-393	179	32	ensures	ensure	VERB
ejpam-393	179	33	that	that	SCONJ
ejpam-393	179	34	the	the	DET
ejpam-393	179	35	right	right	ADJ
ejpam-393	179	36	hand	hand	NOUN
ejpam-393	179	37	side	side	NOUN
ejpam-393	179	38	does	do	AUX
ejpam-393	179	39	not	not	PART
ejpam-393	179	40	depend	depend	VERB
ejpam-393	179	41	on	on	ADP
ejpam-393	179	42	x	x	NOUN
ejpam-393	179	43	)	)	PUNCT
ejpam-393	179	44	.	.	PUNCT
ejpam-393	180	1	this	this	DET
ejpam-393	180	2	move	move	NOUN
ejpam-393	180	3	is	be	AUX
ejpam-393	180	4	called	call	VERB
ejpam-393	180	5	a	a	DET
ejpam-393	180	6	cylindrifier	cylindrifi	ADJ
ejpam-393	180	7	move	move	NOUN
ejpam-393	180	8	and	and	CCONJ
ejpam-393	180	9	is	be	AUX
ejpam-393	180	10	denoted	denote	VERB
ejpam-393	180	11	(	(	PUNCT
ejpam-393	180	12	n	n	X
ejpam-393	180	13	,	,	PUNCT
ejpam-393	180	14	〈	〈	PROPN
ejpam-393	180	15	f0	f0	PROPN
ejpam-393	180	16	,	,	PUNCT
ejpam-393	180	17	.	.	PUNCT
ejpam-393	180	18	.	.	PUNCT
ejpam-393	180	19	.	.	PUNCT
ejpam-393	181	1	fµ−2	fµ−2	NOUN
ejpam-393	181	2	〉	〉	PROPN
ejpam-393	181	3	,	,	PUNCT
ejpam-393	181	4	k	k	PROPN
ejpam-393	181	5	,	,	PUNCT
ejpam-393	181	6	b	b	PROPN
ejpam-393	181	7	,	,	PUNCT
ejpam-393	181	8	l	l	NOUN
ejpam-393	181	9	)	)	PUNCT
ejpam-393	181	10	or	or	CCONJ
ejpam-393	181	11	simply	simply	ADV
ejpam-393	181	12	(	(	PUNCT
ejpam-393	181	13	n	n	X
ejpam-393	181	14	,	,	PUNCT
ejpam-393	181	15	f	f	X
ejpam-393	181	16	,	,	PUNCT
ejpam-393	181	17	k	k	PROPN
ejpam-393	181	18	,	,	PUNCT
ejpam-393	181	19	b	b	PROPN
ejpam-393	181	20	,	,	PUNCT
ejpam-393	181	21	l	l	NOUN
ejpam-393	181	22	)	)	PUNCT
ejpam-393	181	23	.	.	PUNCT
ejpam-393	182	1	in	in	ADP
ejpam-393	182	2	order	order	NOUN
ejpam-393	182	3	to	to	PART
ejpam-393	182	4	make	make	VERB
ejpam-393	182	5	a	a	DET
ejpam-393	182	6	legal	legal	ADJ
ejpam-393	182	7	response	response	NOUN
ejpam-393	182	8	,	,	PUNCT
ejpam-393	182	9	∃	∃	PROPN
ejpam-393	182	10	must	must	AUX
ejpam-393	182	11	play	play	VERB
ejpam-393	182	12	a	a	DET
ejpam-393	182	13	network	network	NOUN
ejpam-393	182	14	m	m	NOUN
ejpam-393	182	15	⊇	⊇	NOUN
ejpam-393	182	16	n	n	PRON
ejpam-393	182	17	such	such	ADJ
ejpam-393	182	18	that	that	SCONJ
ejpam-393	182	19	m	m	PROPN
ejpam-393	182	20	(	(	PUNCT
ejpam-393	182	21	f0	f0	PROPN
ejpam-393	182	22	,	,	PUNCT
ejpam-393	182	23	.	.	PUNCT
ejpam-393	182	24	.	.	PUNCT
ejpam-393	182	25	.	.	PUNCT
ejpam-393	183	1	fi−1	fi−1	PROPN
ejpam-393	183	2	,	,	PUNCT
ejpam-393	183	3	k	k	NOUN
ejpam-393	183	4	,	,	PUNCT
ejpam-393	183	5	fi	fi	NOUN
ejpam-393	183	6	,	,	PUNCT
ejpam-393	183	7	.	.	PUNCT
ejpam-393	183	8	.	.	PUNCT
ejpam-393	183	9	.	.	PUNCT
ejpam-393	184	1	fn−2	fn−2	ADJ
ejpam-393	184	2	)	)	PUNCT
ejpam-393	184	3	)	)	PUNCT
ejpam-393	185	1	=	=	SYM
ejpam-393	185	2	b	b	PROPN
ejpam-393	185	3	and	and	CCONJ
ejpam-393	185	4	nodes(m	nodes(m	NUM
ejpam-393	185	5	)	)	PUNCT
ejpam-393	186	1	=	=	SYM
ejpam-393	186	2	nodes(n)∪	nodes(n)∪	NOUN
ejpam-393	186	3	{	{	PUNCT
ejpam-393	186	4	k	k	NOUN
ejpam-393	186	5	}	}	PUNCT
ejpam-393	186	6	.	.	PUNCT
ejpam-393	187	1	∃	∃	PROPN
ejpam-393	187	2	wins	win	VERB
ejpam-393	187	3	f	f	PROPN
ejpam-393	187	4	m	m	VERB
ejpam-393	187	5	n	n	PROPN
ejpam-393	187	6	(	(	PUNCT
ejpam-393	187	7	α	α	X
ejpam-393	187	8	)	)	PUNCT
ejpam-393	187	9	if	if	SCONJ
ejpam-393	187	10	she	she	PRON
ejpam-393	187	11	responds	respond	VERB
ejpam-393	187	12	with	with	ADP
ejpam-393	187	13	a	a	DET
ejpam-393	187	14	legal	legal	ADJ
ejpam-393	187	15	move	move	NOUN
ejpam-393	187	16	in	in	ADP
ejpam-393	187	17	each	each	PRON
ejpam-393	187	18	of	of	ADP
ejpam-393	187	19	the	the	DET
ejpam-393	187	20	ω	ω	PROPN
ejpam-393	187	21	rounds	round	NOUN
ejpam-393	187	22	.	.	PUNCT
ejpam-393	188	1	if	if	SCONJ
ejpam-393	188	2	she	she	PRON
ejpam-393	188	3	fails	fail	VERB
ejpam-393	188	4	to	to	PART
ejpam-393	188	5	make	make	VERB
ejpam-393	188	6	a	a	DET
ejpam-393	188	7	legal	legal	ADJ
ejpam-393	188	8	response	response	NOUN
ejpam-393	188	9	in	in	ADP
ejpam-393	188	10	any	any	DET
ejpam-393	188	11	round	round	NOUN
ejpam-393	188	12	then	then	ADV
ejpam-393	188	13	∀	∀	NOUN
ejpam-393	188	14	wins	win	NOUN
ejpam-393	188	15	.	.	PUNCT
ejpam-393	189	1	•	•	NUM
ejpam-393	189	2	fix	fix	VERB
ejpam-393	189	3	some	some	DET
ejpam-393	189	4	hyperlabel	hyperlabel	NOUN
ejpam-393	189	5	λ0	λ0	NOUN
ejpam-393	189	6	.	.	PUNCT
ejpam-393	190	1	hn(α	hn(α	PUNCT
ejpam-393	190	2	)	)	PUNCT
ejpam-393	190	3	is	be	AUX
ejpam-393	190	4	a	a	DET
ejpam-393	190	5	game	game	NOUN
ejpam-393	190	6	the	the	DET
ejpam-393	190	7	play	play	NOUN
ejpam-393	190	8	of	of	ADP
ejpam-393	190	9	which	which	PRON
ejpam-393	190	10	consists	consist	VERB
ejpam-393	190	11	of	of	ADP
ejpam-393	190	12	a	a	DET
ejpam-393	190	13	sequence	sequence	NOUN
ejpam-393	190	14	of	of	ADP
ejpam-393	190	15	λ0neat	λ0neat	PROPN
ejpam-393	190	16	hypernetworks	hypernetwork	NOUN
ejpam-393	190	17	n0	n0	PROPN
ejpam-393	190	18	,	,	PUNCT
ejpam-393	190	19	n1	n1	NOUN
ejpam-393	190	20	,	,	PUNCT
ejpam-393	190	21	.	.	PUNCT
ejpam-393	190	22	.	.	PUNCT
ejpam-393	191	1	.	.	PUNCT
ejpam-393	192	1	where	where	SCONJ
ejpam-393	192	2	nodes(ni	nodes(ni	NOUN
ejpam-393	192	3	)	)	PUNCT
ejpam-393	192	4	is	be	AUX
ejpam-393	192	5	a	a	DET
ejpam-393	192	6	finite	finite	NOUN
ejpam-393	192	7	subset	subset	NOUN
ejpam-393	192	8	of	of	ADP
ejpam-393	192	9	ω	ω	PROPN
ejpam-393	192	10	,	,	PUNCT
ejpam-393	192	11	for	for	ADP
ejpam-393	192	12	each	each	DET
ejpam-393	192	13	i	i	PRON
ejpam-393	192	14	<	<	X
ejpam-393	192	15	ω	ω	X
ejpam-393	192	16	.	.	PUNCT
ejpam-393	193	1	in	in	ADP
ejpam-393	193	2	the	the	DET
ejpam-393	193	3	initial	initial	ADJ
ejpam-393	193	4	round	round	NOUN
ejpam-393	193	5	∀	∀	X
ejpam-393	193	6	picks	pick	VERB
ejpam-393	193	7	a	a	DET
ejpam-393	193	8	∈	∈	PROPN
ejpam-393	193	9	α	α	NOUN
ejpam-393	193	10	and	and	CCONJ
ejpam-393	193	11	∃	∃	PROPN
ejpam-393	193	12	must	must	AUX
ejpam-393	193	13	play	play	VERB
ejpam-393	193	14	a	a	DET
ejpam-393	193	15	λ0	λ0	NOUN
ejpam-393	193	16	-	-	PUNCT
ejpam-393	193	17	neat	neat	ADJ
ejpam-393	193	18	hypernetwork	hypernetwork	NOUN
ejpam-393	193	19	n0	n0	NOUN
ejpam-393	193	20	with	with	ADP
ejpam-393	193	21	nodes	node	NOUN
ejpam-393	193	22	contained	contain	VERB
ejpam-393	193	23	in	in	ADP
ejpam-393	193	24	µ	µ	NOUN
ejpam-393	193	25	and	and	CCONJ
ejpam-393	193	26	n0(d̄	n0(d̄	NUM
ejpam-393	193	27	)	)	PUNCT
ejpam-393	194	1	=	=	NOUN
ejpam-393	195	1	a	a	PRON
ejpam-393	195	2	for	for	ADP
ejpam-393	195	3	some	some	DET
ejpam-393	195	4	nodes	node	NOUN
ejpam-393	195	5	d̄	d̄	PROPN
ejpam-393	195	6	∈	∈	PROPN
ejpam-393	196	1	µn0	µn0	PROPN
ejpam-393	196	2	.	.	PUNCT
ejpam-393	197	1	at	at	ADP
ejpam-393	197	2	a	a	DET
ejpam-393	197	3	later	later	ADJ
ejpam-393	197	4	stage	stage	NOUN
ejpam-393	197	5	∀	∀	NOUN
ejpam-393	197	6	can	can	AUX
ejpam-393	197	7	make	make	VERB
ejpam-393	197	8	any	any	DET
ejpam-393	197	9	cylindrifier	cylindrifi	ADJ
ejpam-393	197	10	move	move	NOUN
ejpam-393	197	11	(	(	PUNCT
ejpam-393	197	12	n	n	X
ejpam-393	197	13	,	,	PUNCT
ejpam-393	197	14	f	f	X
ejpam-393	197	15	,	,	PUNCT
ejpam-393	197	16	k	k	PROPN
ejpam-393	197	17	,	,	PUNCT
ejpam-393	197	18	b	b	PROPN
ejpam-393	197	19	,	,	PUNCT
ejpam-393	197	20	l	l	NOUN
ejpam-393	197	21	)	)	PUNCT
ejpam-393	197	22	by	by	ADP
ejpam-393	197	23	picking	pick	VERB
ejpam-393	197	24	a	a	DET
ejpam-393	197	25	previously	previously	ADV
ejpam-393	197	26	played	play	VERB
ejpam-393	197	27	hypernetwork	hypernetwork	NOUN
ejpam-393	197	28	n	n	NOUN
ejpam-393	197	29	and	and	CCONJ
ejpam-393	197	30	f	f	PROPN
ejpam-393	197	31	∈	∈	PROPN
ejpam-393	197	32	n−2nodes(n	n−2nodes(n	NOUN
ejpam-393	197	33	)	)	PUNCT
ejpam-393	197	34	,	,	PUNCT
ejpam-393	197	35	l	l	X
ejpam-393	197	36	<	<	X
ejpam-393	197	37	n	n	X
ejpam-393	197	38	,	,	PUNCT
ejpam-393	197	39	k	k	PROPN
ejpam-393	197	40	∈	∈	PROPN
ejpam-393	197	41	ω	ω	NUM
ejpam-393	197	42	\	\	PROPN
ejpam-393	197	43	nodes(n	nodes(n	PROPN
ejpam-393	197	44	)	)	PUNCT
ejpam-393	197	45	and	and	CCONJ
ejpam-393	197	46	b	b	PROPN
ejpam-393	197	47	≤	≤	NUM
ejpam-393	197	48	cln	cln	PROPN
ejpam-393	197	49	(	(	PUNCT
ejpam-393	197	50	f0	f0	PROPN
ejpam-393	197	51	,	,	PUNCT
ejpam-393	197	52	fl−1	fl−1	PROPN
ejpam-393	197	53	,	,	PUNCT
ejpam-393	197	54	x	x	SYM
ejpam-393	197	55	,	,	PUNCT
ejpam-393	197	56	fn−2	fn−2	PROPN
ejpam-393	197	57	)	)	PUNCT
ejpam-393	197	58	.	.	PUNCT
ejpam-393	198	1	[	[	X
ejpam-393	198	2	in	in	ADP
ejpam-393	198	3	hn	hn	INTJ
ejpam-393	198	4	we	we	PRON
ejpam-393	198	5	require	require	VERB
ejpam-393	198	6	that	that	SCONJ
ejpam-393	198	7	∀	∀	NOUN
ejpam-393	198	8	chooses	choose	VERB
ejpam-393	198	9	k	k	PROPN
ejpam-393	198	10	as	as	ADP
ejpam-393	198	11	a	a	DET
ejpam-393	198	12	’	'	PUNCT
ejpam-393	198	13	new	new	ADJ
ejpam-393	198	14	node	node	NOUN
ejpam-393	198	15	’	'	PUNCT
ejpam-393	198	16	,	,	PUNCT
ejpam-393	198	17	i.e.	i.e.	X
ejpam-393	198	18	not	not	PART
ejpam-393	198	19	in	in	ADP
ejpam-393	198	20	nodes(n	nodes(n	NOUN
ejpam-393	198	21	)	)	PUNCT
ejpam-393	198	22	,	,	PUNCT
ejpam-393	198	23	whereas	whereas	SCONJ
ejpam-393	198	24	in	in	ADP
ejpam-393	198	25	f	f	PROPN
ejpam-393	198	26	m	m	VERB
ejpam-393	198	27	n	n	PROPN
ejpam-393	198	28	for	for	ADP
ejpam-393	198	29	finite	finite	NOUN
ejpam-393	198	30	m	m	VERB
ejpam-393	198	31	it	it	PRON
ejpam-393	198	32	was	be	AUX
ejpam-393	198	33	necessary	necessary	ADJ
ejpam-393	198	34	to	to	PART
ejpam-393	198	35	allow	allow	VERB
ejpam-393	198	36	∀	∀	NOUN
ejpam-393	198	37	to	to	PART
ejpam-393	198	38	’	'	PUNCT
ejpam-393	198	39	reuse	reuse	VERB
ejpam-393	198	40	old	old	ADJ
ejpam-393	198	41	nodes	node	NOUN
ejpam-393	198	42	’	'	PUNCT
ejpam-393	198	43	.	.	PUNCT
ejpam-393	199	1	this	this	PRON
ejpam-393	199	2	makes	make	VERB
ejpam-393	199	3	the	the	DET
ejpam-393	199	4	game	game	NOUN
ejpam-393	199	5	easior	easior	NOUN
ejpam-393	199	6	as	as	ADV
ejpam-393	199	7	far	far	ADV
ejpam-393	199	8	as	as	SCONJ
ejpam-393	199	9	∀	∀	NOUN
ejpam-393	199	10	is	be	AUX
ejpam-393	199	11	concerned	concern	VERB
ejpam-393	199	12	.	.	PUNCT
ejpam-393	199	13	)	)	PUNCT
ejpam-393	200	1	for	for	ADP
ejpam-393	200	2	a	a	DET
ejpam-393	200	3	legal	legal	ADJ
ejpam-393	200	4	response	response	NOUN
ejpam-393	200	5	,	,	PUNCT
ejpam-393	200	6	∃	∃	PROPN
ejpam-393	200	7	must	must	AUX
ejpam-393	200	8	play	play	VERB
ejpam-393	200	9	a	a	DET
ejpam-393	200	10	λ0	λ0	NOUN
ejpam-393	200	11	-	-	PUNCT
ejpam-393	200	12	neat	neat	ADJ
ejpam-393	200	13	hypernetwork	hypernetwork	NOUN
ejpam-393	200	14	m	m	VERB
ejpam-393	200	15	≡k	≡k	NOUN
ejpam-393	200	16	n	n	CCONJ
ejpam-393	200	17	where	where	SCONJ
ejpam-393	200	18	nodes(m	nodes(m	VERB
ejpam-393	200	19	)	)	PUNCT
ejpam-393	200	20	=	=	SYM
ejpam-393	200	21	nodes(n	nodes(n	PROPN
ejpam-393	200	22	)	)	PUNCT
ejpam-393	200	23	∪	∪	NOUN
ejpam-393	200	24	{	{	PUNCT
ejpam-393	200	25	k	k	NOUN
ejpam-393	200	26	}	}	PUNCT
ejpam-393	200	27	and	and	CCONJ
ejpam-393	200	28	m	m	PROPN
ejpam-393	200	29	(	(	PUNCT
ejpam-393	200	30	f0	f0	PROPN
ejpam-393	200	31	,	,	PUNCT
ejpam-393	200	32	fi−1	fi−1	PROPN
ejpam-393	200	33	,	,	PUNCT
ejpam-393	200	34	k	k	PROPN
ejpam-393	200	35	,	,	PUNCT
ejpam-393	200	36	fn−2	fn−2	PROPN
ejpam-393	200	37	)	)	PUNCT
ejpam-393	200	38	=	=	SYM
ejpam-393	200	39	b.	b.	PROPN
ejpam-393	200	40	alternatively	alternatively	ADV
ejpam-393	200	41	,	,	PUNCT
ejpam-393	200	42	∀	∀	PRON
ejpam-393	200	43	can	can	AUX
ejpam-393	200	44	play	play	VERB
ejpam-393	200	45	a	a	DET
ejpam-393	200	46	transformation	transformation	NOUN
ejpam-393	200	47	move	move	NOUN
ejpam-393	200	48	by	by	ADP
ejpam-393	200	49	picking	pick	VERB
ejpam-393	200	50	a	a	DET
ejpam-393	200	51	previously	previously	ADV
ejpam-393	200	52	played	play	VERB
ejpam-393	200	53	hypernetwork	hypernetwork	NOUN
ejpam-393	200	54	n	n	NOUN
ejpam-393	200	55	and	and	CCONJ
ejpam-393	200	56	a	a	DET
ejpam-393	200	57	partial	partial	ADJ
ejpam-393	200	58	,	,	PUNCT
ejpam-393	200	59	finite	finite	PROPN
ejpam-393	200	60	surjection	surjection	PROPN
ejpam-393	200	61	θ	θ	PROPN
ejpam-393	200	62	:	:	PUNCT
ejpam-393	200	63	ω	ω	PROPN
ejpam-393	200	64	→	→	SYM
ejpam-393	200	65	nodes(n	nodes(n	PROPN
ejpam-393	200	66	)	)	PUNCT
ejpam-393	200	67	,	,	PUNCT
ejpam-393	200	68	this	this	DET
ejpam-393	200	69	move	move	NOUN
ejpam-393	200	70	is	be	AUX
ejpam-393	200	71	denoted	denote	VERB
ejpam-393	200	72	(	(	PUNCT
ejpam-393	200	73	n	n	X
ejpam-393	200	74	,	,	PUNCT
ejpam-393	200	75	θ	θ	PROPN
ejpam-393	200	76	)	)	PUNCT
ejpam-393	200	77	.	.	PUNCT
ejpam-393	201	1	∃	∃	PROPN
ejpam-393	201	2	must	must	AUX
ejpam-393	201	3	respond	respond	VERB
ejpam-393	201	4	with	with	ADP
ejpam-393	201	5	nθ	nθ	NOUN
ejpam-393	201	6	.	.	PUNCT
ejpam-393	202	1	finally	finally	ADV
ejpam-393	202	2	,	,	PUNCT
ejpam-393	202	3	∀	∀	X
ejpam-393	202	4	can	can	AUX
ejpam-393	202	5	play	play	VERB
ejpam-393	202	6	an	an	DET
ejpam-393	202	7	amalgamation	amalgamation	NOUN
ejpam-393	202	8	move	move	NOUN
ejpam-393	202	9	by	by	ADP
ejpam-393	202	10	picking	pick	VERB
ejpam-393	202	11	previously	previously	ADV
ejpam-393	202	12	played	play	VERB
ejpam-393	202	13	hypernetworks	hypernetwork	NOUN
ejpam-393	202	14	m	m	VERB
ejpam-393	202	15	,	,	PUNCT
ejpam-393	202	16	n	n	PRON
ejpam-393	202	17	such	such	ADJ
ejpam-393	202	18	that	that	SCONJ
ejpam-393	202	19	m	m	VERB
ejpam-393	202	20	≡nodes(m)∩nodes(n	≡nodes(m)∩nodes(n	ADJ
ejpam-393	202	21	)	)	PUNCT
ejpam-393	202	22	n	n	PROPN
ejpam-393	202	23	and	and	CCONJ
ejpam-393	202	24	nodes(m	nodes(m	NUM
ejpam-393	202	25	)	)	PUNCT
ejpam-393	202	26	∩	∩	NOUN
ejpam-393	202	27	nodes(n	nodes(n	NOUN
ejpam-393	202	28	)	)	PUNCT
ejpam-393	202	29	6=	6=	NUM
ejpam-393	202	30	;	;	PUNCT
ejpam-393	202	31	.	.	PUNCT
ejpam-393	203	1	this	this	DET
ejpam-393	203	2	move	move	NOUN
ejpam-393	203	3	is	be	AUX
ejpam-393	203	4	denoted	denote	VERB
ejpam-393	203	5	(	(	PUNCT
ejpam-393	203	6	m	m	PROPN
ejpam-393	203	7	,	,	PUNCT
ejpam-393	203	8	n	n	CCONJ
ejpam-393	203	9	)	)	PUNCT
ejpam-393	203	10	.	.	PUNCT
ejpam-393	204	1	to	to	PART
ejpam-393	204	2	make	make	VERB
ejpam-393	204	3	a	a	DET
ejpam-393	204	4	legal	legal	ADJ
ejpam-393	204	5	response	response	NOUN
ejpam-393	204	6	,	,	PUNCT
ejpam-393	204	7	∃must	∃must	VERB
ejpam-393	204	8	play	play	VERB
ejpam-393	204	9	a	a	DET
ejpam-393	204	10	λ0	λ0	NOUN
ejpam-393	204	11	-	-	PUNCT
ejpam-393	204	12	neat	neat	ADJ
ejpam-393	204	13	hypernetwork	hypernetwork	NOUN
ejpam-393	204	14	l	l	NOUN
ejpam-393	204	15	extending	extend	VERB
ejpam-393	204	16	m	m	PROPN
ejpam-393	204	17	and	and	CCONJ
ejpam-393	204	18	n	n	CCONJ
ejpam-393	204	19	,	,	PUNCT
ejpam-393	204	20	where	where	SCONJ
ejpam-393	204	21	nodes(l	nodes(l	NOUN
ejpam-393	204	22	)	)	PUNCT
ejpam-393	204	23	=	=	SYM
ejpam-393	204	24	nodes(m)∪	nodes(m)∪	NOUN
ejpam-393	204	25	nodes(n	nodes(n	NOUN
ejpam-393	204	26	)	)	PUNCT
ejpam-393	204	27	.	.	PUNCT
ejpam-393	205	1	again	again	ADV
ejpam-393	205	2	,	,	PUNCT
ejpam-393	205	3	∃	∃	PROPN
ejpam-393	205	4	wins	win	VERB
ejpam-393	205	5	hn(α	hn(α	PUNCT
ejpam-393	205	6	)	)	PUNCT
ejpam-393	205	7	if	if	SCONJ
ejpam-393	205	8	she	she	PRON
ejpam-393	205	9	responds	respond	VERB
ejpam-393	205	10	legally	legally	ADV
ejpam-393	205	11	in	in	ADP
ejpam-393	205	12	each	each	PRON
ejpam-393	205	13	of	of	ADP
ejpam-393	205	14	the	the	DET
ejpam-393	205	15	ω	ω	PROPN
ejpam-393	205	16	rounds	round	NOUN
ejpam-393	205	17	,	,	PUNCT
ejpam-393	205	18	otherwise	otherwise	ADV
ejpam-393	205	19	∀	∀	NOUN
ejpam-393	205	20	wins	win	NOUN
ejpam-393	205	21	.	.	PUNCT
ejpam-393	206	1	t.	t.	PROPN
ejpam-393	206	2	ahmed	ahmed	PROPN
ejpam-393	206	3	/	/	SYM
ejpam-393	206	4	eur	eur	PROPN
ejpam-393	206	5	.	.	PUNCT
ejpam-393	207	1	j.	j.	PROPN
ejpam-393	207	2	pure	pure	PROPN
ejpam-393	207	3	appl	appl	PROPN
ejpam-393	207	4	.	.	PROPN
ejpam-393	207	5	math	math	PROPN
ejpam-393	207	6	,	,	PUNCT
ejpam-393	207	7	3	3	NUM
ejpam-393	207	8	(	(	PUNCT
ejpam-393	207	9	2010	2010	NUM
ejpam-393	207	10	)	)	PUNCT
ejpam-393	207	11	,	,	PUNCT
ejpam-393	207	12	853	853	NUM
ejpam-393	207	13	-	-	SYM
ejpam-393	207	14	880	880	NUM
ejpam-393	207	15	858	858	NUM
ejpam-393	207	16	•	•	NOUN
ejpam-393	207	17	for	for	ADP
ejpam-393	207	18	m	m	PROPN
ejpam-393	207	19	<	<	X
ejpam-393	207	20	ω	ω	NUM
ejpam-393	207	21	the	the	DET
ejpam-393	207	22	game	game	NOUN
ejpam-393	207	23	hm	hm	INTJ
ejpam-393	207	24	,	,	PUNCT
ejpam-393	207	25	n(α	n(α	PROPN
ejpam-393	207	26	)	)	PUNCT
ejpam-393	207	27	is	be	AUX
ejpam-393	207	28	similar	similar	ADJ
ejpam-393	207	29	to	to	ADP
ejpam-393	207	30	hn(α	hn(α	PUNCT
ejpam-393	207	31	)	)	PUNCT
ejpam-393	207	32	but	but	CCONJ
ejpam-393	207	33	play	play	NOUN
ejpam-393	207	34	ends	end	VERB
ejpam-393	207	35	after	after	ADP
ejpam-393	207	36	m	m	PROPN
ejpam-393	207	37	rounds	round	VERB
ejpam-393	207	38	,	,	PUNCT
ejpam-393	207	39	so	so	SCONJ
ejpam-393	207	40	a	a	DET
ejpam-393	207	41	play	play	NOUN
ejpam-393	207	42	of	of	ADP
ejpam-393	207	43	hm	hm	INTJ
ejpam-393	207	44	,	,	PUNCT
ejpam-393	207	45	n(α	n(α	PROPN
ejpam-393	207	46	)	)	PUNCT
ejpam-393	207	47	could	could	AUX
ejpam-393	207	48	be	be	AUX
ejpam-393	207	49	n0	n0	ADJ
ejpam-393	207	50	,	,	PUNCT
ejpam-393	207	51	n1	n1	NOUN
ejpam-393	207	52	,	,	PUNCT
ejpam-393	207	53	.	.	PUNCT
ejpam-393	207	54	.	.	PUNCT
ejpam-393	208	1	.	.	PUNCT
ejpam-393	209	1	,	,	PUNCT
ejpam-393	209	2	nm	nm	INTJ
ejpam-393	209	3	if	if	SCONJ
ejpam-393	209	4	∃	∃	PROPN
ejpam-393	209	5	responds	respond	VERB
ejpam-393	209	6	legally	legally	ADV
ejpam-393	209	7	in	in	ADP
ejpam-393	209	8	each	each	PRON
ejpam-393	209	9	of	of	ADP
ejpam-393	209	10	these	these	DET
ejpam-393	209	11	m	m	NOUN
ejpam-393	209	12	rounds	round	NOUN
ejpam-393	209	13	she	she	PRON
ejpam-393	209	14	wins	win	VERB
ejpam-393	209	15	,	,	PUNCT
ejpam-393	209	16	otherwise	otherwise	ADV
ejpam-393	209	17	∀	∀	NOUN
ejpam-393	209	18	wins	win	NOUN
ejpam-393	209	19	.	.	PUNCT
ejpam-393	210	1	definition	definition	NOUN
ejpam-393	210	2	4	4	NUM
ejpam-393	210	3	.	.	PUNCT
ejpam-393	211	1	for	for	ADP
ejpam-393	211	2	m	m	PROPN
ejpam-393	211	3	≥	≥	NOUN
ejpam-393	211	4	5	5	NUM
ejpam-393	211	5	and	and	CCONJ
ejpam-393	211	6	c	c	NOUN
ejpam-393	211	7	∈	∈	PROPN
ejpam-393	211	8	cam	cam	NOUN
ejpam-393	211	9	,	,	PUNCT
ejpam-393	211	10	if	if	SCONJ
ejpam-393	211	11	a	a	DET
ejpam-393	211	12	⊆	⊆	NUM
ejpam-393	211	13	nrn(c	nrn(c	PROPN
ejpam-393	211	14	)	)	PUNCT
ejpam-393	211	15	is	be	AUX
ejpam-393	211	16	an	an	DET
ejpam-393	211	17	atomic	atomic	ADJ
ejpam-393	211	18	cylindric	cylindric	ADJ
ejpam-393	211	19	algebra	algebra	NOUN
ejpam-393	211	20	and	and	CCONJ
ejpam-393	211	21	n	n	NOUN
ejpam-393	211	22	is	be	AUX
ejpam-393	211	23	an	an	DET
ejpam-393	211	24	a	a	PRON
ejpam-393	211	25	-	-	PUNCT
ejpam-393	211	26	network	network	NOUN
ejpam-393	211	27	then	then	ADV
ejpam-393	211	28	we	we	PRON
ejpam-393	211	29	define	define	VERB
ejpam-393	211	30	bn	bn	NUM
ejpam-393	211	31	∈	∈	ADJ
ejpam-393	211	32	c	c	NOUN
ejpam-393	211	33	by	by	ADP
ejpam-393	211	34	bn	bn	NOUN
ejpam-393	211	35	=	=	SYM
ejpam-393	211	36	∏	∏	PROPN
ejpam-393	211	37	i0,	i0,	PROPN
ejpam-393	211	38	...	...	PUNCT
ejpam-393	211	39	in−1∈nodes(n	in−1∈nodes(n	NOUN
ejpam-393	211	40	)	)	PUNCT
ejpam-393	211	41	si0,	si0,	NOUN
ejpam-393	211	42	...	...	PUNCT
ejpam-393	211	43	in−1	in−1	ADJ
ejpam-393	211	44	n(i0	n(i0	NOUN
ejpam-393	211	45	.	.	PUNCT
ejpam-393	211	46	.	.	PUNCT
ejpam-393	211	47	.	.	PUNCT
ejpam-393	212	1	in−1	in−1	ADJ
ejpam-393	212	2	)	)	PUNCT
ejpam-393	212	3	bn	bn	ADP
ejpam-393	212	4	∈	∈	PROPN
ejpam-393	212	5	c	c	NOUN
ejpam-393	212	6	depends	depend	VERB
ejpam-393	212	7	implicitly	implicitly	ADV
ejpam-393	212	8	on	on	ADP
ejpam-393	212	9	c.	c.	NOUN
ejpam-393	212	10	we	we	PRON
ejpam-393	212	11	write	write	VERB
ejpam-393	212	12	a	a	DET
ejpam-393	212	13	⊆c	⊆c	NOUN
ejpam-393	212	14	b	b	NOUN
ejpam-393	212	15	if	if	SCONJ
ejpam-393	212	16	a	a	DET
ejpam-393	212	17	∈	∈	PROPN
ejpam-393	212	18	sc{b	sc{b	PROPN
ejpam-393	212	19	}	}	PUNCT
ejpam-393	212	20	.	.	PUNCT
ejpam-393	213	1	lemma	lemma	PROPN
ejpam-393	213	2	1	1	X
ejpam-393	213	3	.	.	PUNCT
ejpam-393	214	1	let	let	VERB
ejpam-393	214	2	n	n	PRON
ejpam-393	214	3	<	<	X
ejpam-393	214	4	m	m	VERB
ejpam-393	214	5	and	and	CCONJ
ejpam-393	214	6	let	let	VERB
ejpam-393	214	7	a	a	DET
ejpam-393	214	8	be	be	AUX
ejpam-393	214	9	an	an	DET
ejpam-393	214	10	atomic	atomic	ADJ
ejpam-393	214	11	can	can	AUX
ejpam-393	214	12	,	,	PUNCT
ejpam-393	214	13	a	a	DET
ejpam-393	214	14	⊆c	⊆c	NOUN
ejpam-393	214	15	nrnc	nrnc	NOUN
ejpam-393	214	16	for	for	ADP
ejpam-393	214	17	some	some	DET
ejpam-393	214	18	c	c	PROPN
ejpam-393	214	19	∈	∈	PROPN
ejpam-393	214	20	cam	cam	NOUN
ejpam-393	214	21	.	.	PUNCT
ejpam-393	215	1	for	for	ADP
ejpam-393	215	2	all	all	DET
ejpam-393	215	3	x	x	SYM
ejpam-393	215	4	∈	∈	PROPN
ejpam-393	215	5	c	c	NOUN
ejpam-393	215	6	\	\	X
ejpam-393	215	7	{	{	PUNCT
ejpam-393	215	8	0	0	NUM
ejpam-393	215	9	}	}	PUNCT
ejpam-393	215	10	and	and	CCONJ
ejpam-393	215	11	all	all	DET
ejpam-393	215	12	i0	i0	PROPN
ejpam-393	215	13	,	,	PUNCT
ejpam-393	215	14	.	.	PUNCT
ejpam-393	215	15	.	.	PUNCT
ejpam-393	215	16	.	.	PUNCT
ejpam-393	216	1	in−1	in−1	ADJ
ejpam-393	216	2	<	<	X
ejpam-393	216	3	m	m	VERB
ejpam-393	216	4	there	there	PRON
ejpam-393	216	5	is	be	VERB
ejpam-393	216	6	a	a	DET
ejpam-393	216	7	∈	∈	NOUN
ejpam-393	216	8	at(a	at(a	NOUN
ejpam-393	216	9	)	)	PUNCT
ejpam-393	216	10	such	such	ADJ
ejpam-393	216	11	that	that	DET
ejpam-393	216	12	si0	si0	NOUN
ejpam-393	216	13	...	...	PUNCT
ejpam-393	216	14	in−1	in−1	ADJ
ejpam-393	216	15	a	a	PRON
ejpam-393	216	16	.	.	PUNCT
ejpam-393	217	1	x	x	PUNCT
ejpam-393	217	2	6=	6=	ADP
ejpam-393	217	3	0	0	NUM
ejpam-393	217	4	.	.	PUNCT
ejpam-393	218	1	proof	proof	NOUN
ejpam-393	218	2	.	.	PUNCT
ejpam-393	219	1	we	we	PRON
ejpam-393	219	2	can	can	AUX
ejpam-393	219	3	assume	assume	VERB
ejpam-393	219	4	,	,	PUNCT
ejpam-393	219	5	see	see	VERB
ejpam-393	219	6	definition	definition	NOUN
ejpam-393	219	7	1	1	NUM
ejpam-393	219	8	,	,	PUNCT
ejpam-393	219	9	that	that	PRON
ejpam-393	219	10	si0,	si0,	ADV
ejpam-393	219	11	...	...	PUNCT
ejpam-393	219	12	in−1	in−1	ADJ
ejpam-393	219	13	consists	consist	VERB
ejpam-393	219	14	only	only	ADV
ejpam-393	219	15	of	of	ADP
ejpam-393	219	16	substitutions	substitution	NOUN
ejpam-393	219	17	,	,	PUNCT
ejpam-393	219	18	since	since	SCONJ
ejpam-393	219	19	cm	cm	NOUN
ejpam-393	219	20	.	.	PUNCT
ejpam-393	219	21	.	.	PUNCT
ejpam-393	220	1	.	.	PUNCT
ejpam-393	221	1	cm−1	cm−1	NOUN
ejpam-393	221	2	.	.	PUNCT
ejpam-393	221	3	.	.	PUNCT
ejpam-393	221	4	.	.	PUNCT
ejpam-393	222	1	cn	cn	X
ejpam-393	222	2	x	x	PUNCT
ejpam-393	223	1	=	=	PUNCT
ejpam-393	223	2	x	x	PUNCT
ejpam-393	223	3	for	for	ADP
ejpam-393	223	4	every	every	DET
ejpam-393	223	5	x	x	SYM
ejpam-393	223	6	∈	∈	NOUN
ejpam-393	223	7	a.we	a.we	NOUN
ejpam-393	223	8	have	have	VERB
ejpam-393	223	9	si	si	PROPN
ejpam-393	223	10	j	j	PROPN
ejpam-393	223	11	is	be	AUX
ejpam-393	223	12	a	a	DET
ejpam-393	223	13	completely	completely	ADV
ejpam-393	223	14	additive	additive	ADJ
ejpam-393	223	15	operator	operator	NOUN
ejpam-393	223	16	(	(	PUNCT
ejpam-393	223	17	any	any	DET
ejpam-393	223	18	i	i	PROPN
ejpam-393	223	19	,	,	PUNCT
ejpam-393	223	20	j	j	PROPN
ejpam-393	223	21	)	)	PUNCT
ejpam-393	223	22	,	,	PUNCT
ejpam-393	223	23	hence	hence	ADV
ejpam-393	223	24	si0,	si0,	PRON
ejpam-393	223	25	...	...	PUNCT
ejpam-393	223	26	iµ−1	iµ−1	PROPN
ejpam-393	223	27	is	be	AUX
ejpam-393	223	28	too	too	ADV
ejpam-393	223	29	(	(	PUNCT
ejpam-393	223	30	see	see	VERB
ejpam-393	223	31	definition	definition	NOUN
ejpam-393	223	32	1	1	NUM
ejpam-393	223	33	)	)	PUNCT
ejpam-393	223	34	.	.	PUNCT
ejpam-393	224	1	so	so	ADV
ejpam-393	224	2	∑	∑	ADV
ejpam-393	224	3	{	{	PUNCT
ejpam-393	224	4	si0	si0	NOUN
ejpam-393	224	5	...	...	PUNCT
ejpam-393	224	6	in−1	in−1	ADJ
ejpam-393	224	7	a	a	DET
ejpam-393	224	8	:	:	PUNCT
ejpam-393	224	9	a	a	DET
ejpam-393	224	10	∈	∈	NOUN
ejpam-393	224	11	at(a	at(a	NOUN
ejpam-393	224	12	)	)	PUNCT
ejpam-393	224	13	}	}	PUNCT
ejpam-393	224	14	=	=	SYM
ejpam-393	224	15	si0	si0	NOUN
ejpam-393	224	16	...	...	PUNCT
ejpam-393	224	17	in−1	in−1	ADJ
ejpam-393	224	18	∑	∑	PUNCT
ejpam-393	224	19	at(a	at(a	NUM
ejpam-393	224	20	)	)	PUNCT
ejpam-393	224	21	=	=	SYM
ejpam-393	224	22	si0	si0	NOUN
ejpam-393	224	23	...	...	PUNCT
ejpam-393	224	24	in−1	in−1	ADJ
ejpam-393	224	25	1=	1=	NUM
ejpam-393	224	26	1	1	NUM
ejpam-393	224	27	,	,	PUNCT
ejpam-393	224	28	for	for	ADP
ejpam-393	224	29	any	any	DET
ejpam-393	224	30	i0	i0	PROPN
ejpam-393	224	31	,	,	PUNCT
ejpam-393	224	32	.	.	PUNCT
ejpam-393	224	33	.	.	PUNCT
ejpam-393	224	34	.	.	PUNCT
ejpam-393	225	1	in−1	in−1	ADJ
ejpam-393	225	2	<	<	X
ejpam-393	225	3	n.	n.	PROPN
ejpam-393	225	4	let	let	VERB
ejpam-393	225	5	x	x	X
ejpam-393	225	6	∈	∈	PROPN
ejpam-393	225	7	c\{0	c\{0	PROPN
ejpam-393	225	8	}	}	PUNCT
ejpam-393	225	9	.	.	PUNCT
ejpam-393	226	1	it	it	PRON
ejpam-393	226	2	is	be	AUX
ejpam-393	226	3	impossible	impossible	ADJ
ejpam-393	226	4	that	that	SCONJ
ejpam-393	226	5	si0	si0	NOUN
ejpam-393	226	6	...	...	PUNCT
ejpam-393	226	7	in−1	in−1	ADJ
ejpam-393	226	8	.	.	PUNCT
ejpam-393	227	1	x	x	X
ejpam-393	227	2	=	=	SYM
ejpam-393	227	3	0	0	NUM
ejpam-393	227	4	for	for	ADP
ejpam-393	227	5	all	all	DET
ejpam-393	227	6	a	a	DET
ejpam-393	227	7	∈	∈	NOUN
ejpam-393	227	8	at(a	at(a	NOUN
ejpam-393	227	9	)	)	PUNCT
ejpam-393	227	10	because	because	SCONJ
ejpam-393	227	11	this	this	PRON
ejpam-393	227	12	would	would	AUX
ejpam-393	227	13	imply	imply	VERB
ejpam-393	227	14	that	that	PRON
ejpam-393	227	15	1−x	1−x	NUM
ejpam-393	227	16	was	be	AUX
ejpam-393	227	17	an	an	DET
ejpam-393	227	18	upper	upper	ADJ
ejpam-393	227	19	bound	bind	VERB
ejpam-393	227	20	for	for	ADP
ejpam-393	227	21	{	{	PUNCT
ejpam-393	227	22	si0	si0	NOUN
ejpam-393	227	23	...	...	PUNCT
ejpam-393	227	24	in−1	in−1	ADJ
ejpam-393	227	25	a	a	DET
ejpam-393	227	26	:	:	PUNCT
ejpam-393	227	27	a	a	DET
ejpam-393	227	28	∈	∈	NOUN
ejpam-393	227	29	at(a	at(a	NUM
ejpam-393	227	30	)	)	PUNCT
ejpam-393	227	31	}	}	PUNCT
ejpam-393	228	1	,	,	PUNCT
ejpam-393	228	2	contradicting	contradict	VERB
ejpam-393	228	3	∑	∑	ADP
ejpam-393	228	4	{	{	PUNCT
ejpam-393	228	5	si0	si0	NOUN
ejpam-393	228	6	...	...	PUNCT
ejpam-393	228	7	in−1	in−1	ADJ
ejpam-393	228	8	a	a	DET
ejpam-393	228	9	:	:	PUNCT
ejpam-393	228	10	a	a	DET
ejpam-393	228	11	∈	∈	NOUN
ejpam-393	228	12	at(a	at(a	NOUN
ejpam-393	228	13	)	)	PUNCT
ejpam-393	228	14	}	}	PUNCT
ejpam-393	228	15	=	=	SYM
ejpam-393	229	1	1	1	X
ejpam-393	229	2	.	.	PUNCT
ejpam-393	229	3	lemma	lemma	PROPN
ejpam-393	229	4	2	2	X
ejpam-393	229	5	.	.	PUNCT
ejpam-393	230	1	let	let	VERB
ejpam-393	230	2	n	n	CCONJ
ejpam-393	230	3	<	<	X
ejpam-393	230	4	m	m	PRON
ejpam-393	230	5	and	and	CCONJ
ejpam-393	230	6	let	let	VERB
ejpam-393	230	7	a	a	DET
ejpam-393	230	8	⊆c	⊆c	NOUN
ejpam-393	230	9	nrnc	nrnc	NOUN
ejpam-393	230	10	be	be	AUX
ejpam-393	230	11	an	an	DET
ejpam-393	230	12	atomic	atomic	ADJ
ejpam-393	230	13	can	can	AUX
ejpam-393	230	14	1	1	NUM
ejpam-393	230	15	.	.	PUNCT
ejpam-393	231	1	for	for	ADP
ejpam-393	231	2	any	any	DET
ejpam-393	231	3	x	x	SYM
ejpam-393	231	4	∈	∈	PROPN
ejpam-393	231	5	c	c	NOUN
ejpam-393	231	6	\	\	X
ejpam-393	231	7	{	{	PUNCT
ejpam-393	231	8	0	0	NUM
ejpam-393	231	9	}	}	PUNCT
ejpam-393	231	10	and	and	CCONJ
ejpam-393	231	11	any	any	DET
ejpam-393	231	12	finite	finite	NOUN
ejpam-393	231	13	set	set	VERB
ejpam-393	231	14	i	i	PRON
ejpam-393	231	15	⊆	⊆	NUM
ejpam-393	231	16	m	m	VERB
ejpam-393	231	17	there	there	PRON
ejpam-393	231	18	is	be	VERB
ejpam-393	231	19	a	a	DET
ejpam-393	231	20	network	network	NOUN
ejpam-393	231	21	n	n	CCONJ
ejpam-393	231	22	such	such	ADJ
ejpam-393	231	23	that	that	DET
ejpam-393	231	24	nodes(n	nodes(n	NOUN
ejpam-393	231	25	)	)	PUNCT
ejpam-393	231	26	=	=	PUNCT
ejpam-393	232	1	i	i	PRON
ejpam-393	232	2	and	and	CCONJ
ejpam-393	232	3	x	x	INTJ
ejpam-393	232	4	.	.	PUNCT
ejpam-393	233	1	bn	bn	PROPN
ejpam-393	233	2	6=	6=	NUM
ejpam-393	233	3	0	0	NUM
ejpam-393	233	4	.	.	PROPN
ejpam-393	234	1	2	2	NUM
ejpam-393	234	2	.	.	X
ejpam-393	234	3	for	for	ADP
ejpam-393	234	4	any	any	DET
ejpam-393	234	5	networks	network	NOUN
ejpam-393	234	6	m	m	VERB
ejpam-393	234	7	,	,	PUNCT
ejpam-393	234	8	n	n	CCONJ
ejpam-393	234	9	if	if	SCONJ
ejpam-393	234	10	bm	bm	PROPN
ejpam-393	234	11	.	.	PUNCT
ejpam-393	235	1	bn	bn	PROPN
ejpam-393	236	1	6=	6=	NUM
ejpam-393	236	2	0	0	PUNCT
ejpam-393	236	3	then	then	ADV
ejpam-393	236	4	m	m	VERB
ejpam-393	236	5	≡nodes(m)∩nodes(n	≡nodes(m)∩nodes(n	ADJ
ejpam-393	236	6	)	)	PUNCT
ejpam-393	236	7	n.	n.	NOUN
ejpam-393	236	8	proof	proof	NOUN
ejpam-393	236	9	.	.	PUNCT
ejpam-393	237	1	the	the	DET
ejpam-393	237	2	proof	proof	NOUN
ejpam-393	237	3	of	of	ADP
ejpam-393	237	4	the	the	DET
ejpam-393	237	5	first	first	ADJ
ejpam-393	237	6	part	part	NOUN
ejpam-393	237	7	is	be	AUX
ejpam-393	237	8	based	base	VERB
ejpam-393	237	9	on	on	ADP
ejpam-393	237	10	repeated	repeat	VERB
ejpam-393	237	11	use	use	NOUN
ejpam-393	237	12	of	of	ADP
ejpam-393	237	13	lemma	lemma	PROPN
ejpam-393	237	14	1	1	NUM
ejpam-393	237	15	.	.	PUNCT
ejpam-393	238	1	we	we	PRON
ejpam-393	238	2	define	define	VERB
ejpam-393	238	3	the	the	DET
ejpam-393	238	4	edge	edge	NOUN
ejpam-393	238	5	labeling	labeling	NOUN
ejpam-393	238	6	of	of	ADP
ejpam-393	238	7	n	n	DET
ejpam-393	238	8	one	one	NUM
ejpam-393	238	9	edge	edge	NOUN
ejpam-393	238	10	at	at	ADP
ejpam-393	238	11	a	a	DET
ejpam-393	238	12	time	time	NOUN
ejpam-393	238	13	.	.	PUNCT
ejpam-393	239	1	initially	initially	ADV
ejpam-393	239	2	no	no	DET
ejpam-393	239	3	hyperedges	hyperedge	NOUN
ejpam-393	239	4	are	be	AUX
ejpam-393	239	5	labeled	label	VERB
ejpam-393	239	6	.	.	PUNCT
ejpam-393	240	1	suppose	suppose	VERB
ejpam-393	240	2	e	e	X
ejpam-393	240	3	⊆	⊆	NUM
ejpam-393	240	4	nodes(n)×	nodes(n)×	PROPN
ejpam-393	240	5	nodes(n	nodes(n	PROPN
ejpam-393	240	6	)	)	PUNCT
ejpam-393	240	7	.	.	PUNCT
ejpam-393	240	8	.	.	PUNCT
ejpam-393	241	1	.×	.×	PROPN
ejpam-393	241	2	nodes(n	nodes(n	PROPN
ejpam-393	241	3	)	)	PUNCT
ejpam-393	241	4	is	be	AUX
ejpam-393	241	5	the	the	DET
ejpam-393	241	6	set	set	NOUN
ejpam-393	241	7	of	of	ADP
ejpam-393	241	8	labeled	label	VERB
ejpam-393	241	9	hyper	hyper	ADJ
ejpam-393	241	10	edges	edge	NOUN
ejpam-393	241	11	of	of	ADP
ejpam-393	241	12	n	n	PROPN
ejpam-393	241	13	(	(	PUNCT
ejpam-393	241	14	initially	initially	ADV
ejpam-393	241	15	e	e	X
ejpam-393	241	16	=	=	PUNCT
ejpam-393	241	17	;)	;)	PUNCT
ejpam-393	241	18	and	and	CCONJ
ejpam-393	241	19	x	x	INTJ
ejpam-393	241	20	.	.	PUNCT
ejpam-393	242	1	∏	∏	PROPN
ejpam-393	242	2	c̄∈e	c̄∈e	PROPN
ejpam-393	242	3	sc̄n(c̄	sc̄n(c̄	PROPN
ejpam-393	242	4	)	)	PUNCT
ejpam-393	242	5	6=	6=	ADP
ejpam-393	242	6	0	0	X
ejpam-393	242	7	.	.	X
ejpam-393	242	8	pick	pick	VERB
ejpam-393	242	9	d̄	d̄	NOUN
ejpam-393	242	10	such	such	ADJ
ejpam-393	242	11	that	that	DET
ejpam-393	242	12	d̄	d̄	PROPN
ejpam-393	242	13	6∈	6∈	PROPN
ejpam-393	242	14	e.	e.	PROPN
ejpam-393	242	15	by	by	ADP
ejpam-393	242	16	lemma	lemma	PROPN
ejpam-393	242	17	1	1	NUM
ejpam-393	242	18	there	there	PRON
ejpam-393	242	19	is	be	VERB
ejpam-393	242	20	a	a	DET
ejpam-393	242	21	∈	∈	NOUN
ejpam-393	242	22	at(a	at(a	PUNCT
ejpam-393	242	23	)	)	PUNCT
ejpam-393	242	24	such	such	ADJ
ejpam-393	242	25	that	that	SCONJ
ejpam-393	242	26	x	x	X
ejpam-393	242	27	.	.	PUNCT
ejpam-393	242	28	∏	∏	PROPN
ejpam-393	242	29	c̄∈e	c̄∈e	PROPN
ejpam-393	242	30	sc̄n(c̄	sc̄n(c̄	PROPN
ejpam-393	242	31	)	)	PUNCT
ejpam-393	242	32	.	.	PUNCT
ejpam-393	243	1	sd̄	sd̄	VERB
ejpam-393	243	2	a	a	PRON
ejpam-393	243	3	6=	6=	NUM
ejpam-393	243	4	0	0	NUM
ejpam-393	243	5	.	.	NOUN
ejpam-393	243	6	include	include	VERB
ejpam-393	243	7	the	the	DET
ejpam-393	243	8	edge	edge	NOUN
ejpam-393	243	9	d̄	d̄	NOUN
ejpam-393	243	10	in	in	ADP
ejpam-393	243	11	e.	e.	PROPN
ejpam-393	243	12	eventually	eventually	ADV
ejpam-393	243	13	,	,	PUNCT
ejpam-393	243	14	all	all	DET
ejpam-393	243	15	edges	edge	NOUN
ejpam-393	243	16	will	will	AUX
ejpam-393	243	17	be	be	AUX
ejpam-393	243	18	labeled	label	VERB
ejpam-393	243	19	,	,	PUNCT
ejpam-393	243	20	so	so	SCONJ
ejpam-393	243	21	we	we	PRON
ejpam-393	243	22	obtain	obtain	VERB
ejpam-393	243	23	a	a	DET
ejpam-393	243	24	completely	completely	ADV
ejpam-393	243	25	labeled	label	VERB
ejpam-393	243	26	graph	graph	NOUN
ejpam-393	243	27	n	n	X
ejpam-393	243	28	with	with	ADP
ejpam-393	243	29	bn	bn	PROPN
ejpam-393	243	30	6=	6=	NUM
ejpam-393	243	31	0	0	NUM
ejpam-393	243	32	.	.	PUNCT
ejpam-393	244	1	it	it	PRON
ejpam-393	244	2	is	be	AUX
ejpam-393	244	3	easily	easily	ADV
ejpam-393	244	4	checked	check	VERB
ejpam-393	244	5	that	that	SCONJ
ejpam-393	244	6	n	n	NOUN
ejpam-393	244	7	is	be	AUX
ejpam-393	244	8	a	a	DET
ejpam-393	244	9	network	network	NOUN
ejpam-393	244	10	.	.	PUNCT
ejpam-393	245	1	for	for	ADP
ejpam-393	245	2	the	the	DET
ejpam-393	245	3	second	second	ADJ
ejpam-393	245	4	part	part	NOUN
ejpam-393	245	5	,	,	PUNCT
ejpam-393	245	6	if	if	SCONJ
ejpam-393	245	7	it	it	PRON
ejpam-393	245	8	is	be	AUX
ejpam-393	245	9	not	not	PART
ejpam-393	245	10	true	true	ADJ
ejpam-393	245	11	that	that	SCONJ
ejpam-393	245	12	m	m	VERB
ejpam-393	245	13	≡nodes(m)∩nodes(n	≡nodes(m)∩nodes(n	ADJ
ejpam-393	245	14	)	)	PUNCT
ejpam-393	245	15	n	n	CCONJ
ejpam-393	245	16	then	then	ADV
ejpam-393	245	17	there	there	PRON
ejpam-393	245	18	are	be	VERB
ejpam-393	245	19	is	be	AUX
ejpam-393	245	20	c̄	c̄	PROPN
ejpam-393	245	21	∈n−1	∈n−1	PROPN
ejpam-393	245	22	nodes(m	nodes(m	PROPN
ejpam-393	245	23	)	)	PUNCT
ejpam-393	245	24	∩	∩	NOUN
ejpam-393	245	25	nodes(n	nodes(n	NOUN
ejpam-393	245	26	)	)	PUNCT
ejpam-393	245	27	such	such	ADJ
ejpam-393	245	28	that	that	DET
ejpam-393	245	29	m(c̄	m(c̄	NOUN
ejpam-393	245	30	)	)	PUNCT
ejpam-393	245	31	6=	6=	NUM
ejpam-393	245	32	n(c̄	n(c̄	NOUN
ejpam-393	245	33	)	)	PUNCT
ejpam-393	245	34	.	.	PUNCT
ejpam-393	246	1	since	since	SCONJ
ejpam-393	246	2	edges	edge	NOUN
ejpam-393	246	3	are	be	AUX
ejpam-393	246	4	labeled	label	VERB
ejpam-393	246	5	by	by	ADP
ejpam-393	246	6	atoms	atom	NOUN
ejpam-393	246	7	we	we	PRON
ejpam-393	246	8	have	have	VERB
ejpam-393	246	9	m(c̄	m(c̄	NOUN
ejpam-393	246	10	)	)	PUNCT
ejpam-393	246	11	·	·	PUNCT
ejpam-393	247	1	n(c̄	n(c̄	NOUN
ejpam-393	247	2	)	)	PUNCT
ejpam-393	247	3	=	=	SYM
ejpam-393	247	4	0	0	NUM
ejpam-393	247	5	,	,	PUNCT
ejpam-393	247	6	so	so	SCONJ
ejpam-393	247	7	0=	0=	PRON
ejpam-393	247	8	sc̄0=	sc̄0=	NOUN
ejpam-393	247	9	sc̄	sc̄	NOUN
ejpam-393	247	10	m(c̄	m(c̄	NOUN
ejpam-393	247	11	)	)	PUNCT
ejpam-393	247	12	.	.	PUNCT
ejpam-393	248	1	sc̄n(c̄)≥	sc̄n(c̄)≥	PROPN
ejpam-393	248	2	bm	bm	PROPN
ejpam-393	248	3	.	.	PUNCT
ejpam-393	249	1	bn	bn	INTJ
ejpam-393	249	2	.	.	PUNCT
ejpam-393	250	1	lemma	lemma	PROPN
ejpam-393	250	2	3	3	X
ejpam-393	250	3	.	.	PUNCT
ejpam-393	251	1	let	let	AUX
ejpam-393	251	2	let	let	VERB
ejpam-393	251	3	m	m	PRON
ejpam-393	251	4	>	>	X
ejpam-393	251	5	n.	n.	PROPN
ejpam-393	251	6	let	let	VERB
ejpam-393	251	7	c	c	PROPN
ejpam-393	251	8	∈	∈	PROPN
ejpam-393	251	9	cam	cam	VERB
ejpam-393	251	10	and	and	CCONJ
ejpam-393	251	11	let	let	VERB
ejpam-393	251	12	a	a	DET
ejpam-393	251	13	⊆nrn(c	⊆nrn(c	NOUN
ejpam-393	251	14	)	)	PUNCT
ejpam-393	251	15	be	be	AUX
ejpam-393	251	16	atomic	atomic	ADJ
ejpam-393	251	17	.	.	PUNCT
ejpam-393	252	1	let	let	VERB
ejpam-393	252	2	n	n	PRON
ejpam-393	252	3	be	be	AUX
ejpam-393	252	4	a	a	DET
ejpam-393	252	5	network	network	NOUN
ejpam-393	252	6	over	over	ADP
ejpam-393	252	7	a	a	PRON
ejpam-393	252	8	and	and	CCONJ
ejpam-393	252	9	i	i	PRON
ejpam-393	252	10	,	,	PUNCT
ejpam-393	252	11	j	j	PROPN
ejpam-393	252	12	<	<	X
ejpam-393	252	13	n.	n.	PROPN
ejpam-393	252	14	1	1	NUM
ejpam-393	252	15	.	.	PUNCT
ejpam-393	253	1	if	if	SCONJ
ejpam-393	253	2	i	i	PRON
ejpam-393	253	3	6∈	6∈	PROPN
ejpam-393	253	4	nodes(n	nodes(n	PROPN
ejpam-393	253	5	)	)	PUNCT
ejpam-393	253	6	then	then	ADV
ejpam-393	253	7	ci	ci	PROPN
ejpam-393	253	8	bn	bn	PROPN
ejpam-393	253	9	=	=	PROPN
ejpam-393	253	10	bn	bn	PROPN
ejpam-393	253	11	.	.	PUNCT
ejpam-393	254	1	t.	t.	PROPN
ejpam-393	254	2	ahmed	ahmed	PROPN
ejpam-393	254	3	/	/	SYM
ejpam-393	254	4	eur	eur	PROPN
ejpam-393	254	5	.	.	PUNCT
ejpam-393	255	1	j.	j.	PROPN
ejpam-393	255	2	pure	pure	PROPN
ejpam-393	255	3	appl	appl	PROPN
ejpam-393	255	4	.	.	PROPN
ejpam-393	255	5	math	math	PROPN
ejpam-393	255	6	,	,	PUNCT
ejpam-393	255	7	3	3	NUM
ejpam-393	255	8	(	(	PUNCT
ejpam-393	255	9	2010	2010	NUM
ejpam-393	255	10	)	)	PUNCT
ejpam-393	255	11	,	,	PUNCT
ejpam-393	255	12	853	853	NUM
ejpam-393	255	13	-	-	SYM
ejpam-393	255	14	880	880	NUM
ejpam-393	255	15	859	859	NUM
ejpam-393	255	16	2.øn	2.øn	NUM
ejpam-393	255	17	id−	id−	SYM
ejpam-393	255	18	j	j	PROPN
ejpam-393	255	19	≥	≥	X
ejpam-393	255	20	bn	bn	NOUN
ejpam-393	255	21	.	.	PROPN
ejpam-393	256	1	3	3	X
ejpam-393	256	2	.	.	X
ejpam-393	257	1	if	if	SCONJ
ejpam-393	257	2	i	i	PRON
ejpam-393	257	3	6∈	6∈	PROPN
ejpam-393	257	4	nodes(n	nodes(n	PROPN
ejpam-393	257	5	)	)	PUNCT
ejpam-393	257	6	and	and	CCONJ
ejpam-393	257	7	j	j	PROPN
ejpam-393	257	8	∈	∈	PROPN
ejpam-393	257	9	nodes(n	nodes(n	PROPN
ejpam-393	257	10	)	)	PUNCT
ejpam-393	257	11	then	then	ADV
ejpam-393	257	12	bn	bn	X
ejpam-393	257	13	6=	6=	ADP
ejpam-393	257	14	0→ùn[i/	0→ùn[i/	PROPN
ejpam-393	257	15	j	j	PROPN
ejpam-393	257	16	]	]	X
ejpam-393	257	17	6=	6=	ADP
ejpam-393	257	18	0	0	NUM
ejpam-393	257	19	.	.	PUNCT
ejpam-393	257	20	where	where	SCONJ
ejpam-393	257	21	n[i/	n[i/	PROPN
ejpam-393	257	22	j	j	X
ejpam-393	257	23	]	]	X
ejpam-393	257	24	=	=	SYM
ejpam-393	257	25	n	n	PRON
ejpam-393	257	26	◦	◦	NOUN
ejpam-393	258	1	[	[	X
ejpam-393	258	2	i|	i|	PROPN
ejpam-393	258	3	j	j	PROPN
ejpam-393	258	4	]	]	X
ejpam-393	258	5	4	4	X
ejpam-393	258	6	.	.	PUNCT
ejpam-393	259	1	if	if	SCONJ
ejpam-393	259	2	θ	θ	PROPN
ejpam-393	259	3	is	be	AUX
ejpam-393	259	4	any	any	DET
ejpam-393	259	5	partial	partial	ADJ
ejpam-393	259	6	,	,	PUNCT
ejpam-393	259	7	finite	finite	PROPN
ejpam-393	259	8	map	map	NOUN
ejpam-393	259	9	n→	n→	PUNCT
ejpam-393	259	10	n	n	CCONJ
ejpam-393	259	11	and	and	CCONJ
ejpam-393	259	12	if	if	SCONJ
ejpam-393	259	13	nodes(n	nodes(n	PROPN
ejpam-393	259	14	)	)	PUNCT
ejpam-393	259	15	is	be	AUX
ejpam-393	259	16	a	a	DET
ejpam-393	259	17	proper	proper	ADJ
ejpam-393	259	18	subset	subset	NOUN
ejpam-393	259	19	of	of	ADP
ejpam-393	259	20	n	n	CCONJ
ejpam-393	259	21	,	,	PUNCT
ejpam-393	259	22	then	then	ADV
ejpam-393	259	23	bn	bn	NOUN
ejpam-393	259	24	6=	6=	PROPN
ejpam-393	259	25	0→dnθ	0→dnθ	PROPN
ejpam-393	259	26	6=	6=	PRON
ejpam-393	259	27	0	0	X
ejpam-393	259	28	.	.	PUNCT
ejpam-393	260	1	proof	proof	NOUN
ejpam-393	260	2	.	.	PUNCT
ejpam-393	261	1	the	the	DET
ejpam-393	261	2	first	first	ADJ
ejpam-393	261	3	part	part	NOUN
ejpam-393	261	4	is	be	AUX
ejpam-393	261	5	easy	easy	ADJ
ejpam-393	261	6	.	.	PUNCT
ejpam-393	262	1	the	the	DET
ejpam-393	262	2	second	second	ADJ
ejpam-393	262	3	part	part	NOUN
ejpam-393	262	4	is	be	AUX
ejpam-393	262	5	by	by	ADP
ejpam-393	262	6	definition	definition	NOUN
ejpam-393	262	7	of	of	ADP
ejpam-393	262	8	b.	b.	PROPN
ejpam-393	262	9	for	for	ADP
ejpam-393	262	10	the	the	DET
ejpam-393	262	11	third	third	ADJ
ejpam-393	262	12	part	part	NOUN
ejpam-393	262	13	suppose	suppose	VERB
ejpam-393	262	14	bn	bn	ADP
ejpam-393	262	15	6=	6=	NUM
ejpam-393	262	16	0	0	NUM
ejpam-393	262	17	.	.	PUNCT
ejpam-393	263	1	since	since	SCONJ
ejpam-393	263	2	i	i	PRON
ejpam-393	263	3	6∈	6∈	PROPN
ejpam-393	263	4	nodes(n	nodes(n	PROPN
ejpam-393	263	5	)	)	PUNCT
ejpam-393	263	6	,	,	PUNCT
ejpam-393	263	7	by	by	ADP
ejpam-393	263	8	part	part	NOUN
ejpam-393	263	9	1	1	NUM
ejpam-393	263	10	,	,	PUNCT
ejpam-393	263	11	we	we	PRON
ejpam-393	263	12	have	have	VERB
ejpam-393	263	13	ci	ci	NOUN
ejpam-393	263	14	bn	bn	PROPN
ejpam-393	263	15	=	=	PROPN
ejpam-393	263	16	bn	bn	PROPN
ejpam-393	263	17	.	.	PUNCT
ejpam-393	264	1	by	by	ADP
ejpam-393	264	2	cylindric	cylindric	ADJ
ejpam-393	264	3	algebra	algebra	NOUN
ejpam-393	264	4	axioms	axiom	NOUN
ejpam-393	264	5	it	it	PRON
ejpam-393	264	6	follows	follow	VERB
ejpam-393	264	7	that	that	PRON
ejpam-393	264	8	bn	bn	INTJ
ejpam-393	264	9	.	.	PUNCT
ejpam-393	265	1	di	di	PROPN
ejpam-393	265	2	j	j	PROPN
ejpam-393	265	3	6=	6=	PROPN
ejpam-393	265	4	0	0	NUM
ejpam-393	265	5	.	.	PUNCT
ejpam-393	266	1	by	by	ADP
ejpam-393	266	2	lemma	lemma	PROPN
ejpam-393	266	3	2	2	NUM
ejpam-393	266	4	there	there	PRON
ejpam-393	266	5	is	be	VERB
ejpam-393	266	6	a	a	DET
ejpam-393	266	7	network	network	NOUN
ejpam-393	266	8	m	m	VERB
ejpam-393	266	9	where	where	SCONJ
ejpam-393	266	10	nodes(m	nodes(m	NOUN
ejpam-393	266	11	)	)	PUNCT
ejpam-393	266	12	=	=	SYM
ejpam-393	266	13	nodes(n)∪	nodes(n)∪	NOUN
ejpam-393	266	14	{	{	PUNCT
ejpam-393	266	15	i	i	NOUN
ejpam-393	266	16	}	}	PUNCT
ejpam-393	266	17	such	such	ADJ
ejpam-393	266	18	that	that	SCONJ
ejpam-393	266	19	bm	bm	PROPN
ejpam-393	266	20	.bn	.bn	PUNCT
ejpam-393	266	21	.	.	PUNCT
ejpam-393	267	1	di	di	PROPN
ejpam-393	267	2	j	j	PROPN
ejpam-393	267	3	6=	6=	PROPN
ejpam-393	267	4	0	0	NUM
ejpam-393	267	5	.	.	PUNCT
ejpam-393	268	1	by	by	ADP
ejpam-393	268	2	lemma	lemma	PROPN
ejpam-393	268	3	2	2	NUM
ejpam-393	268	4	we	we	PRON
ejpam-393	268	5	have	have	VERB
ejpam-393	268	6	m	m	PROPN
ejpam-393	268	7	⊇	⊇	NOUN
ejpam-393	268	8	n	n	PROPN
ejpam-393	268	9	and	and	CCONJ
ejpam-393	268	10	m(i	m(i	PROPN
ejpam-393	268	11	,	,	PUNCT
ejpam-393	268	12	j	j	NOUN
ejpam-393	268	13	)	)	PUNCT
ejpam-393	268	14	≤	≤	NUM
ejpam-393	268	15	1′.	1′.	NOUN
ejpam-393	268	16	it	it	PRON
ejpam-393	268	17	follows	follow	VERB
ejpam-393	268	18	that	that	SCONJ
ejpam-393	268	19	m	m	VERB
ejpam-393	268	20	=	=	SYM
ejpam-393	269	1	n[i/	n[i/	PROPN
ejpam-393	269	2	j	j	PROPN
ejpam-393	269	3	]	]	X
ejpam-393	269	4	.	.	PUNCT
ejpam-393	270	1	henceùn[i/	henceùn[i/	PROPN
ejpam-393	270	2	j	j	PROPN
ejpam-393	270	3	]	]	X
ejpam-393	270	4	6=	6=	ADP
ejpam-393	270	5	0	0	NUM
ejpam-393	270	6	.	.	PUNCT
ejpam-393	271	1	for	for	ADP
ejpam-393	271	2	the	the	DET
ejpam-393	271	3	final	final	ADJ
ejpam-393	271	4	part	part	NOUN
ejpam-393	271	5	(	(	PUNCT
ejpam-393	271	6	cf	cf	NOUN
ejpam-393	271	7	.	.	PUNCT
ejpam-393	272	1	[	[	X
ejpam-393	272	2	9	9	NUM
ejpam-393	272	3	,	,	PUNCT
ejpam-393	272	4	lemma	lemma	PROPN
ejpam-393	272	5	13.29	13.29	NUM
ejpam-393	272	6	]	]	PUNCT
ejpam-393	272	7	)	)	PUNCT
ejpam-393	272	8	,	,	PUNCT
ejpam-393	272	9	since	since	SCONJ
ejpam-393	272	10	there	there	PRON
ejpam-393	272	11	is	be	VERB
ejpam-393	272	12	k	k	PROPN
ejpam-393	272	13	∈	∈	PROPN
ejpam-393	272	14	n	n	CCONJ
ejpam-393	272	15	\	\	PROPN
ejpam-393	272	16	nodes(n	nodes(n	PROPN
ejpam-393	272	17	)	)	PUNCT
ejpam-393	272	18	,	,	PUNCT
ejpam-393	272	19	θ	θ	PROPN
ejpam-393	272	20	can	can	AUX
ejpam-393	272	21	be	be	AUX
ejpam-393	272	22	expressed	express	VERB
ejpam-393	272	23	as	as	ADP
ejpam-393	272	24	a	a	DET
ejpam-393	272	25	product	product	NOUN
ejpam-393	272	26	σ0σ1	σ0σ1	X
ejpam-393	272	27	.	.	PUNCT
ejpam-393	272	28	.	.	PUNCT
ejpam-393	273	1	.σt	.σt	PUNCT
ejpam-393	274	1	of	of	ADP
ejpam-393	274	2	maps	map	NOUN
ejpam-393	274	3	such	such	ADJ
ejpam-393	274	4	that	that	PRON
ejpam-393	274	5	,	,	PUNCT
ejpam-393	274	6	for	for	ADP
ejpam-393	274	7	s	s	PROPN
ejpam-393	274	8	≤	≤	PROPN
ejpam-393	274	9	t	t	PROPN
ejpam-393	274	10	,	,	PUNCT
ejpam-393	274	11	we	we	PRON
ejpam-393	274	12	have	have	VERB
ejpam-393	274	13	either	either	CCONJ
ejpam-393	274	14	σs	σs	ADP
ejpam-393	274	15	=	=	PUNCT
ejpam-393	274	16	id−i	id−i	PROPN
ejpam-393	274	17	for	for	ADP
ejpam-393	274	18	some	some	PRON
ejpam-393	274	19	i	i	PRON
ejpam-393	274	20	<	<	X
ejpam-393	274	21	n	n	NOUN
ejpam-393	274	22	or	or	CCONJ
ejpam-393	274	23	σs	σs	ADP
ejpam-393	274	24	=	=	PUNCT
ejpam-393	275	1	[	[	X
ejpam-393	275	2	i/	i/	PRON
ejpam-393	275	3	j	j	X
ejpam-393	275	4	]	]	X
ejpam-393	275	5	for	for	ADP
ejpam-393	275	6	some	some	DET
ejpam-393	275	7	i	i	PROPN
ejpam-393	275	8	,	,	PUNCT
ejpam-393	275	9	j	j	PROPN
ejpam-393	275	10	<	<	X
ejpam-393	275	11	n	n	PROPN
ejpam-393	275	12	and	and	CCONJ
ejpam-393	275	13	where	where	SCONJ
ejpam-393	276	1	i	i	PRON
ejpam-393	276	2	6∈	6∈	PROPN
ejpam-393	276	3	nodes(nσ0	nodes(nσ0	PROPN
ejpam-393	276	4	.	.	PUNCT
ejpam-393	276	5	.	.	PUNCT
ejpam-393	277	1	.σs−1	.σs−1	ADP
ejpam-393	277	2	)	)	PUNCT
ejpam-393	277	3	.	.	PUNCT
ejpam-393	278	1	now	now	ADV
ejpam-393	278	2	apply	apply	VERB
ejpam-393	278	3	the	the	DET
ejpam-393	278	4	previous	previous	ADJ
ejpam-393	278	5	parts	part	NOUN
ejpam-393	278	6	of	of	ADP
ejpam-393	278	7	the	the	DET
ejpam-393	278	8	lemma	lemma	PROPN
ejpam-393	278	9	.	.	PUNCT
ejpam-393	279	1	we	we	PRON
ejpam-393	279	2	now	now	ADV
ejpam-393	279	3	prove	prove	VERB
ejpam-393	279	4	two	two	NUM
ejpam-393	279	5	theorems	theorem	NOUN
ejpam-393	279	6	relating	relate	VERB
ejpam-393	279	7	neat	neat	ADJ
ejpam-393	279	8	embeddings	embedding	NOUN
ejpam-393	279	9	to	to	ADP
ejpam-393	279	10	the	the	DET
ejpam-393	279	11	games	game	NOUN
ejpam-393	279	12	we	we	PRON
ejpam-393	279	13	defined	define	VERB
ejpam-393	279	14	:	:	PUNCT
ejpam-393	279	15	theorem	theorem	NOUN
ejpam-393	279	16	2	2	NUM
ejpam-393	279	17	.	.	PUNCT
ejpam-393	280	1	let	let	VERB
ejpam-393	280	2	n	n	PRON
ejpam-393	280	3	<	<	X
ejpam-393	280	4	m	m	PROPN
ejpam-393	280	5	,	,	PUNCT
ejpam-393	280	6	and	and	CCONJ
ejpam-393	280	7	let	let	VERB
ejpam-393	280	8	a	a	PRON
ejpam-393	280	9	be	be	AUX
ejpam-393	280	10	a	a	DET
ejpam-393	280	11	cam	cam	NOUN
ejpam-393	280	12	.	.	PUNCT
ejpam-393	281	1	if	if	SCONJ
ejpam-393	281	2	a	a	DET
ejpam-393	281	3	∈	∈	PROPN
ejpam-393	281	4	scnrncam	scnrncam	NOUN
ejpam-393	281	5	,	,	PUNCT
ejpam-393	281	6	then	then	ADV
ejpam-393	281	7	∃	∃	PROPN
ejpam-393	281	8	has	have	VERB
ejpam-393	281	9	a	a	DET
ejpam-393	281	10	winning	win	VERB
ejpam-393	281	11	strategy	strategy	NOUN
ejpam-393	281	12	in	in	ADP
ejpam-393	281	13	f	f	PROPN
ejpam-393	281	14	m(ata	m(ata	PROPN
ejpam-393	281	15	)	)	PUNCT
ejpam-393	281	16	.	.	PUNCT
ejpam-393	282	1	proof	proof	NOUN
ejpam-393	282	2	.	.	PUNCT
ejpam-393	283	1	if	if	SCONJ
ejpam-393	283	2	a	a	DET
ejpam-393	283	3	⊆	⊆	NUM
ejpam-393	283	4	nrnc	nrnc	NOUN
ejpam-393	283	5	for	for	ADP
ejpam-393	283	6	some	some	DET
ejpam-393	283	7	c	c	PROPN
ejpam-393	283	8	∈	∈	PROPN
ejpam-393	283	9	cam	cam	NOUN
ejpam-393	283	10	then	then	ADV
ejpam-393	283	11	∃	∃	PROPN
ejpam-393	283	12	always	always	ADV
ejpam-393	283	13	plays	play	VERB
ejpam-393	283	14	hypernetworks	hypernetwork	NOUN
ejpam-393	283	15	n	n	X
ejpam-393	283	16	with	with	ADP
ejpam-393	283	17	nodes(n	nodes(n	NOUN
ejpam-393	283	18	)	)	PUNCT
ejpam-393	283	19	⊆	⊆	NUM
ejpam-393	283	20	n	n	ADP
ejpam-393	283	21	such	such	ADJ
ejpam-393	283	22	that	that	PRON
ejpam-393	283	23	bn	bn	PROPN
ejpam-393	283	24	6=	6=	NUM
ejpam-393	283	25	0	0	NUM
ejpam-393	283	26	.	.	PUNCT
ejpam-393	284	1	in	in	ADP
ejpam-393	284	2	more	more	ADJ
ejpam-393	284	3	detail	detail	NOUN
ejpam-393	284	4	,	,	PUNCT
ejpam-393	284	5	in	in	ADP
ejpam-393	284	6	the	the	DET
ejpam-393	284	7	initial	initial	ADJ
ejpam-393	284	8	round	round	NOUN
ejpam-393	284	9	,	,	PUNCT
ejpam-393	284	10	let	let	VERB
ejpam-393	284	11	∀	∀	PRON
ejpam-393	284	12	play	play	VERB
ejpam-393	284	13	a	a	DET
ejpam-393	284	14	∈	∈	PROPN
ejpam-393	284	15	ata	ata	NOUN
ejpam-393	284	16	.	.	PUNCT
ejpam-393	285	1	∃	∃	PROPN
ejpam-393	285	2	play	play	VERB
ejpam-393	285	3	a	a	DET
ejpam-393	285	4	network	network	NOUN
ejpam-393	285	5	n	n	X
ejpam-393	285	6	with	with	ADP
ejpam-393	285	7	n(0	n(0	PROPN
ejpam-393	285	8	,	,	PUNCT
ejpam-393	285	9	.	.	PUNCT
ejpam-393	285	10	.	.	PUNCT
ejpam-393	285	11	.	.	PUNCT
ejpam-393	286	1	n−	n−	NOUN
ejpam-393	286	2	1	1	NUM
ejpam-393	286	3	)	)	PUNCT
ejpam-393	286	4	=	=	SYM
ejpam-393	286	5	a.	a.	NOUN
ejpam-393	286	6	then	then	ADV
ejpam-393	286	7	bn	bn	ADV
ejpam-393	286	8	=	=	PUNCT
ejpam-393	286	9	a	a	PRON
ejpam-393	286	10	6=	6=	NUM
ejpam-393	286	11	0	0	NUM
ejpam-393	286	12	.	.	PUNCT
ejpam-393	287	1	at	at	ADP
ejpam-393	287	2	a	a	DET
ejpam-393	287	3	later	later	ADJ
ejpam-393	287	4	stage	stage	NOUN
ejpam-393	287	5	suppose	suppose	VERB
ejpam-393	287	6	∀	∀	NOUN
ejpam-393	287	7	plays	play	VERB
ejpam-393	287	8	the	the	DET
ejpam-393	287	9	cylindrifier	cylindrifi	ADJ
ejpam-393	287	10	move	move	NOUN
ejpam-393	287	11	(	(	PUNCT
ejpam-393	287	12	n	n	NOUN
ejpam-393	287	13	,	,	PUNCT
ejpam-393	287	14	〈	〈	PROPN
ejpam-393	287	15	f0	f0	PROPN
ejpam-393	287	16	,	,	PUNCT
ejpam-393	287	17	.	.	PUNCT
ejpam-393	287	18	.	.	PUNCT
ejpam-393	287	19	.	.	PUNCT
ejpam-393	288	1	fµ−2	fµ−2	NOUN
ejpam-393	288	2	〉	〉	PROPN
ejpam-393	288	3	,	,	PUNCT
ejpam-393	288	4	k	k	PROPN
ejpam-393	288	5	,	,	PUNCT
ejpam-393	288	6	b	b	PROPN
ejpam-393	288	7	,	,	PUNCT
ejpam-393	288	8	l	l	NOUN
ejpam-393	288	9	)	)	PUNCT
ejpam-393	288	10	by	by	ADP
ejpam-393	288	11	picking	pick	VERB
ejpam-393	288	12	a	a	DET
ejpam-393	288	13	previously	previously	ADV
ejpam-393	288	14	played	play	VERB
ejpam-393	288	15	hypernetwork	hypernetwork	NOUN
ejpam-393	288	16	n	n	NOUN
ejpam-393	288	17	and	and	CCONJ
ejpam-393	288	18	fi	fi	NOUN
ejpam-393	288	19	∈	∈	PROPN
ejpam-393	288	20	nodes(n	nodes(n	PROPN
ejpam-393	288	21	)	)	PUNCT
ejpam-393	288	22	,	,	PUNCT
ejpam-393	288	23	l	l	X
ejpam-393	288	24	<	<	X
ejpam-393	288	25	µ	µ	X
ejpam-393	288	26	,	,	PUNCT
ejpam-393	288	27	k	k	PROPN
ejpam-393	288	28	/∈	/∈	PUNCT
ejpam-393	288	29	{	{	PUNCT
ejpam-393	289	1	fi	fi	NOUN
ejpam-393	289	2	:	:	PUNCT
ejpam-393	289	3	i	i	PRON
ejpam-393	289	4	<	<	X
ejpam-393	289	5	n	n	CCONJ
ejpam-393	289	6	−	−	NOUN
ejpam-393	289	7	2	2	NUM
ejpam-393	289	8	}	}	PUNCT
ejpam-393	289	9	,	,	PUNCT
ejpam-393	289	10	and	and	CCONJ
ejpam-393	289	11	b	b	X
ejpam-393	289	12	≤	≤	NUM
ejpam-393	289	13	cln	cln	PROPN
ejpam-393	289	14	(	(	PUNCT
ejpam-393	289	15	f0	f0	PROPN
ejpam-393	289	16	,	,	PUNCT
ejpam-393	289	17	.	.	PUNCT
ejpam-393	289	18	.	.	PUNCT
ejpam-393	289	19	.	.	PUNCT
ejpam-393	290	1	fi−1	fi−1	PROPN
ejpam-393	290	2	,	,	PUNCT
ejpam-393	290	3	x	x	NOUN
ejpam-393	290	4	,	,	PUNCT
ejpam-393	290	5	fn−2	fn−2	PROPN
ejpam-393	290	6	)	)	PUNCT
ejpam-393	290	7	.	.	PUNCT
ejpam-393	291	1	let	let	VERB
ejpam-393	291	2	ā	ā	ADJ
ejpam-393	291	3	=	=	PUNCT
ejpam-393	291	4	〈	〈	NOUN
ejpam-393	291	5	f0	f0	PROPN
ejpam-393	291	6	.	.	PUNCT
ejpam-393	291	7	.	.	PUNCT
ejpam-393	291	8	.	.	PUNCT
ejpam-393	292	1	fl−1	fl−1	PROPN
ejpam-393	292	2	,	,	PUNCT
ejpam-393	292	3	k	k	X
ejpam-393	292	4	.	.	PUNCT
ejpam-393	292	5	.	.	PUNCT
ejpam-393	292	6	.	.	PUNCT
ejpam-393	293	1	fn−2	fn−2	ADJ
ejpam-393	293	2	〉	〉	NOUN
ejpam-393	293	3	.	.	PUNCT
ejpam-393	294	1	then	then	ADV
ejpam-393	294	2	ck	ck	PROPN
ejpam-393	294	3	bn	bn	PROPN
ejpam-393	294	4	·	·	PUNCT
ejpam-393	294	5	sā	sā	NOUN
ejpam-393	294	6	b	b	X
ejpam-393	294	7	6=	6=	PROPN
ejpam-393	294	8	0	0	NUM
ejpam-393	294	9	.	.	PUNCT
ejpam-393	295	1	by	by	ADP
ejpam-393	295	2	1	1	NUM
ejpam-393	295	3	there	there	PRON
ejpam-393	295	4	is	be	VERB
ejpam-393	295	5	a	a	DET
ejpam-393	295	6	network	network	NOUN
ejpam-393	295	7	m	m	VERB
ejpam-393	295	8	such	such	ADJ
ejpam-393	295	9	that	that	SCONJ
ejpam-393	295	10	bm	bm	PROPN
ejpam-393	295	11	.ôckn	.ôckn	ADJ
ejpam-393	295	12	·	·	PUNCT
ejpam-393	295	13	sā	sā	NOUN
ejpam-393	295	14	b	b	X
ejpam-393	295	15	6=	6=	PROPN
ejpam-393	295	16	0	0	NUM
ejpam-393	295	17	.	.	PUNCT
ejpam-393	296	1	hence	hence	ADV
ejpam-393	296	2	m	m	PROPN
ejpam-393	296	3	(	(	PUNCT
ejpam-393	296	4	f0	f0	PROPN
ejpam-393	296	5	,	,	PUNCT
ejpam-393	296	6	k	k	PROPN
ejpam-393	296	7	,	,	PUNCT
ejpam-393	296	8	fn−2	fn−2	PROPN
ejpam-393	296	9	)	)	PUNCT
ejpam-393	296	10	=	=	SYM
ejpam-393	296	11	b.	b.	PROPN
ejpam-393	296	12	theorem	theorem	NOUN
ejpam-393	296	13	3	3	X
ejpam-393	296	14	.	.	PUNCT
ejpam-393	297	1	let	let	VERB
ejpam-393	297	2	α	α	PRON
ejpam-393	297	3	be	be	AUX
ejpam-393	297	4	a	a	DET
ejpam-393	297	5	countable	countable	ADJ
ejpam-393	297	6	can	can	AUX
ejpam-393	297	7	atom	atom	NOUN
ejpam-393	297	8	structure	structure	NOUN
ejpam-393	297	9	.	.	PUNCT
ejpam-393	298	1	if	if	SCONJ
ejpam-393	298	2	∃	∃	PROPN
ejpam-393	298	3	has	have	VERB
ejpam-393	298	4	a	a	DET
ejpam-393	298	5	winning	win	VERB
ejpam-393	298	6	strategy	strategy	NOUN
ejpam-393	298	7	in	in	ADP
ejpam-393	298	8	hn(α	hn(α	PUNCT
ejpam-393	298	9	)	)	PUNCT
ejpam-393	298	10	then	then	ADV
ejpam-393	298	11	there	there	PRON
ejpam-393	298	12	is	be	VERB
ejpam-393	298	13	a	a	DET
ejpam-393	298	14	representable	representable	ADJ
ejpam-393	298	15	cylindric	cylindric	ADJ
ejpam-393	298	16	algebra	algebra	NOUN
ejpam-393	298	17	c	c	PROPN
ejpam-393	298	18	of	of	ADP
ejpam-393	298	19	dimension	dimension	NOUN
ejpam-393	298	20	ω	ω	PROPN
ejpam-393	298	21	such	such	ADJ
ejpam-393	298	22	that	that	SCONJ
ejpam-393	298	23	nrnc	nrnc	NOUN
ejpam-393	298	24	is	be	AUX
ejpam-393	298	25	atomic	atomic	ADJ
ejpam-393	298	26	and	and	CCONJ
ejpam-393	298	27	atnrnc	atnrnc	NOUN
ejpam-393	298	28	∼=	∼=	PART
ejpam-393	298	29	α	α	NOUN
ejpam-393	298	30	.	.	PUNCT
ejpam-393	299	1	proof	proof	NOUN
ejpam-393	299	2	.	.	PUNCT
ejpam-393	300	1	suppose	suppose	VERB
ejpam-393	300	2	∃	∃	PROPN
ejpam-393	300	3	has	have	VERB
ejpam-393	300	4	a	a	DET
ejpam-393	300	5	winning	win	VERB
ejpam-393	300	6	strategy	strategy	NOUN
ejpam-393	300	7	in	in	ADP
ejpam-393	300	8	h(α	h(α	ADJ
ejpam-393	300	9	)	)	PUNCT
ejpam-393	300	10	.	.	PUNCT
ejpam-393	301	1	fix	fix	VERB
ejpam-393	301	2	some	some	PRON
ejpam-393	301	3	a	a	DET
ejpam-393	301	4	∈	∈	PROPN
ejpam-393	301	5	α	α	NOUN
ejpam-393	301	6	.	.	PUNCT
ejpam-393	302	1	we	we	PRON
ejpam-393	302	2	can	can	AUX
ejpam-393	302	3	define	define	VERB
ejpam-393	302	4	a	a	DET
ejpam-393	302	5	nested	nested	ADJ
ejpam-393	302	6	sequence	sequence	NOUN
ejpam-393	302	7	n0	n0	NOUN
ejpam-393	302	8	⊆	⊆	NUM
ejpam-393	302	9	n1	n1	NOUN
ejpam-393	302	10	.	.	PUNCT
ejpam-393	302	11	.	.	PUNCT
ejpam-393	303	1	.	.	PUNCT
ejpam-393	304	1	of	of	ADP
ejpam-393	304	2	hypernetworks	hypernetwork	NOUN
ejpam-393	304	3	where	where	SCONJ
ejpam-393	304	4	n0	n0	PROPN
ejpam-393	304	5	is	be	AUX
ejpam-393	304	6	∃	∃	PROPN
ejpam-393	304	7	’s	’s	PART
ejpam-393	304	8	response	response	NOUN
ejpam-393	304	9	to	to	ADP
ejpam-393	304	10	the	the	DET
ejpam-393	304	11	initial	initial	ADJ
ejpam-393	304	12	∀-move	∀-move	VERB
ejpam-393	304	13	a	a	PRON
ejpam-393	304	14	,	,	PUNCT
ejpam-393	304	15	requiring	require	VERB
ejpam-393	304	16	that	that	SCONJ
ejpam-393	304	17	1	1	X
ejpam-393	304	18	.	.	PUNCT
ejpam-393	305	1	if	if	SCONJ
ejpam-393	305	2	nr	nr	PRON
ejpam-393	305	3	is	be	AUX
ejpam-393	305	4	in	in	ADP
ejpam-393	305	5	the	the	DET
ejpam-393	305	6	sequence	sequence	NOUN
ejpam-393	305	7	and	and	CCONJ
ejpam-393	305	8	and	and	CCONJ
ejpam-393	305	9	b	b	PROPN
ejpam-393	305	10	≤	≤	PROPN
ejpam-393	305	11	clnr	clnr	NOUN
ejpam-393	305	12	(	(	PUNCT
ejpam-393	305	13	〈	〈	PROPN
ejpam-393	305	14	f0	f0	PROPN
ejpam-393	305	15	,	,	PUNCT
ejpam-393	305	16	fn−2	fn−2	ADJ
ejpam-393	305	17	〉	〉	NOUN
ejpam-393	305	18	.	.	PUNCT
ejpam-393	305	19	.	.	PUNCT
ejpam-393	306	1	.	.	PUNCT
ejpam-393	307	1	,	,	PUNCT
ejpam-393	307	2	x	x	X
ejpam-393	307	3	,	,	PUNCT
ejpam-393	307	4	fn−2	fn−2	PROPN
ejpam-393	307	5	)	)	PUNCT
ejpam-393	307	6	.	.	PUNCT
ejpam-393	308	1	then	then	ADV
ejpam-393	308	2	there	there	PRON
ejpam-393	308	3	is	be	VERB
ejpam-393	308	4	s	s	PROPN
ejpam-393	308	5	≥	≥	NOUN
ejpam-393	308	6	r	r	NOUN
ejpam-393	308	7	and	and	CCONJ
ejpam-393	308	8	d	d	PROPN
ejpam-393	308	9	∈	∈	PROPN
ejpam-393	308	10	nodes(ns	nodes(ns	PROPN
ejpam-393	308	11	)	)	PUNCT
ejpam-393	308	12	such	such	ADJ
ejpam-393	308	13	that	that	SCONJ
ejpam-393	308	14	ns	ns	PROPN
ejpam-393	308	15	(	(	PUNCT
ejpam-393	308	16	f0	f0	PROPN
ejpam-393	308	17	,	,	PUNCT
ejpam-393	308	18	fi−1	fi−1	PROPN
ejpam-393	308	19	,	,	PUNCT
ejpam-393	308	20	d	d	PROPN
ejpam-393	308	21	,	,	PUNCT
ejpam-393	308	22	fn−2	fn−2	PROPN
ejpam-393	308	23	)	)	PUNCT
ejpam-393	308	24	=	=	SYM
ejpam-393	308	25	b.	b.	PROPN
ejpam-393	309	1	2	2	X
ejpam-393	309	2	.	.	PUNCT
ejpam-393	310	1	if	if	SCONJ
ejpam-393	310	2	nr	nr	PRON
ejpam-393	310	3	is	be	AUX
ejpam-393	310	4	in	in	ADP
ejpam-393	310	5	the	the	DET
ejpam-393	310	6	sequence	sequence	NOUN
ejpam-393	310	7	and	and	CCONJ
ejpam-393	310	8	θ	θ	PROPN
ejpam-393	310	9	is	be	AUX
ejpam-393	310	10	any	any	DET
ejpam-393	310	11	partial	partial	ADJ
ejpam-393	310	12	isomorphism	isomorphism	NOUN
ejpam-393	310	13	of	of	ADP
ejpam-393	310	14	nr	nr	PRON
ejpam-393	310	15	then	then	ADV
ejpam-393	310	16	there	there	PRON
ejpam-393	310	17	is	be	VERB
ejpam-393	310	18	s	s	PROPN
ejpam-393	310	19	≥	≥	NOUN
ejpam-393	310	20	r	r	NOUN
ejpam-393	310	21	and	and	CCONJ
ejpam-393	310	22	a	a	DET
ejpam-393	310	23	partial	partial	ADJ
ejpam-393	310	24	isomorphism	isomorphism	NOUN
ejpam-393	310	25	θ+	θ+	PUNCT
ejpam-393	310	26	of	of	ADP
ejpam-393	310	27	ns	ns	NUM
ejpam-393	310	28	extending	extend	VERB
ejpam-393	310	29	θ	θ	PROPN
ejpam-393	310	30	such	such	ADJ
ejpam-393	310	31	that	that	SCONJ
ejpam-393	310	32	rng(θ+)⊇	rng(θ+)⊇	PROPN
ejpam-393	310	33	nodes(nr	nodes(nr	PROPN
ejpam-393	310	34	)	)	PUNCT
ejpam-393	310	35	.	.	PUNCT
ejpam-393	311	1	since	since	SCONJ
ejpam-393	311	2	α	α	PROPN
ejpam-393	311	3	is	be	AUX
ejpam-393	311	4	countable	countable	ADJ
ejpam-393	311	5	there	there	PRON
ejpam-393	311	6	are	be	VERB
ejpam-393	311	7	countably	countably	ADV
ejpam-393	311	8	many	many	ADJ
ejpam-393	311	9	requirements	requirement	NOUN
ejpam-393	311	10	to	to	PART
ejpam-393	311	11	extend	extend	VERB
ejpam-393	311	12	.	.	PUNCT
ejpam-393	312	1	since	since	SCONJ
ejpam-393	312	2	the	the	DET
ejpam-393	312	3	sequence	sequence	NOUN
ejpam-393	312	4	of	of	ADP
ejpam-393	312	5	networks	network	NOUN
ejpam-393	312	6	is	be	AUX
ejpam-393	312	7	nested	nest	VERB
ejpam-393	312	8	,	,	PUNCT
ejpam-393	312	9	these	these	DET
ejpam-393	312	10	requirements	requirement	NOUN
ejpam-393	312	11	to	to	PART
ejpam-393	312	12	extend	extend	VERB
ejpam-393	312	13	remain	remain	VERB
ejpam-393	312	14	in	in	ADP
ejpam-393	312	15	all	all	DET
ejpam-393	312	16	subsequent	subsequent	ADJ
ejpam-393	312	17	rounds	round	NOUN
ejpam-393	312	18	.	.	PUNCT
ejpam-393	313	1	so	so	SCONJ
ejpam-393	313	2	that	that	SCONJ
ejpam-393	313	3	we	we	PRON
ejpam-393	313	4	can	can	AUX
ejpam-393	313	5	schedule	schedule	VERB
ejpam-393	313	6	these	these	DET
ejpam-393	313	7	requirements	requirement	NOUN
ejpam-393	313	8	to	to	PART
ejpam-393	313	9	extend	extend	VERB
ejpam-393	313	10	so	so	SCONJ
ejpam-393	313	11	that	that	SCONJ
ejpam-393	313	12	eventually	eventually	ADV
ejpam-393	313	13	,	,	PUNCT
ejpam-393	313	14	every	every	DET
ejpam-393	313	15	requirement	requirement	NOUN
ejpam-393	313	16	gets	get	VERB
ejpam-393	313	17	t.	t.	PROPN
ejpam-393	313	18	ahmed	ahmed	PROPN
ejpam-393	313	19	/	/	SYM
ejpam-393	313	20	eur	eur	PROPN
ejpam-393	313	21	.	.	PUNCT
ejpam-393	314	1	j.	j.	PROPN
ejpam-393	314	2	pure	pure	PROPN
ejpam-393	314	3	appl	appl	PROPN
ejpam-393	314	4	.	.	PROPN
ejpam-393	314	5	math	math	PROPN
ejpam-393	314	6	,	,	PUNCT
ejpam-393	314	7	3	3	NUM
ejpam-393	314	8	(	(	PUNCT
ejpam-393	314	9	2010	2010	NUM
ejpam-393	314	10	)	)	PUNCT
ejpam-393	314	11	,	,	PUNCT
ejpam-393	314	12	853	853	NUM
ejpam-393	314	13	-	-	SYM
ejpam-393	314	14	880	880	NUM
ejpam-393	314	15	860	860	NUM
ejpam-393	314	16	dealt	deal	VERB
ejpam-393	314	17	with	with	ADP
ejpam-393	314	18	.	.	PUNCT
ejpam-393	315	1	if	if	SCONJ
ejpam-393	315	2	we	we	PRON
ejpam-393	315	3	are	be	AUX
ejpam-393	315	4	required	require	VERB
ejpam-393	315	5	to	to	PART
ejpam-393	315	6	find	find	VERB
ejpam-393	315	7	k	k	PROPN
ejpam-393	315	8	and	and	CCONJ
ejpam-393	315	9	nr+1	nr+1	PROPN
ejpam-393	315	10	⊃	⊃	PROPN
ejpam-393	315	11	nr	nr	PRON
ejpam-393	316	1	such	such	ADJ
ejpam-393	316	2	that	that	SCONJ
ejpam-393	316	3	nr+1	nr+1	PROPN
ejpam-393	316	4	(	(	PUNCT
ejpam-393	316	5	f0	f0	PROPN
ejpam-393	316	6	,	,	PUNCT
ejpam-393	316	7	k	k	PROPN
ejpam-393	316	8	,	,	PUNCT
ejpam-393	316	9	fn−2	fn−2	PROPN
ejpam-393	316	10	)	)	PUNCT
ejpam-393	316	11	=	=	SYM
ejpam-393	316	12	b	b	PROPN
ejpam-393	316	13	then	then	ADV
ejpam-393	316	14	let	let	VERB
ejpam-393	316	15	k	k	PROPN
ejpam-393	316	16	∈ω	∈ω	DET
ejpam-393	316	17	\nodes(nr	\nodes(nr	PROPN
ejpam-393	316	18	)	)	PUNCT
ejpam-393	316	19	be	be	AUX
ejpam-393	316	20	least	least	ADJ
ejpam-393	316	21	possible	possible	ADJ
ejpam-393	316	22	for	for	ADP
ejpam-393	316	23	definiteness	definiteness	NOUN
ejpam-393	316	24	,	,	PUNCT
ejpam-393	316	25	and	and	CCONJ
ejpam-393	316	26	let	let	VERB
ejpam-393	316	27	nr+1	nr+1	PRON
ejpam-393	316	28	be	be	AUX
ejpam-393	316	29	∃	∃	PROPN
ejpam-393	316	30	’s	’s	PART
ejpam-393	316	31	response	response	NOUN
ejpam-393	316	32	using	use	VERB
ejpam-393	316	33	her	her	PRON
ejpam-393	316	34	winning	winning	NOUN
ejpam-393	316	35	strategy	strategy	NOUN
ejpam-393	316	36	,	,	PUNCT
ejpam-393	316	37	to	to	ADP
ejpam-393	316	38	the	the	DET
ejpam-393	316	39	∀move	∀move	NOUN
ejpam-393	316	40	nr	nr	PROPN
ejpam-393	316	41	,	,	PUNCT
ejpam-393	316	42	(	(	PUNCT
ejpam-393	316	43	f0	f0	PROPN
ejpam-393	316	44	,	,	PUNCT
ejpam-393	316	45	.	.	PUNCT
ejpam-393	316	46	.	.	PUNCT
ejpam-393	316	47	.	.	PUNCT
ejpam-393	317	1	fn−1	fn−1	ADJ
ejpam-393	317	2	)	)	PUNCT
ejpam-393	317	3	,	,	PUNCT
ejpam-393	317	4	k	k	PROPN
ejpam-393	317	5	,	,	PUNCT
ejpam-393	317	6	b	b	PROPN
ejpam-393	317	7	,	,	PUNCT
ejpam-393	317	8	l	l	NOUN
ejpam-393	317	9	)	)	PUNCT
ejpam-393	317	10	.	.	PUNCT
ejpam-393	318	1	for	for	ADP
ejpam-393	318	2	an	an	DET
ejpam-393	318	3	extension	extension	NOUN
ejpam-393	318	4	of	of	ADP
ejpam-393	318	5	type	type	NOUN
ejpam-393	318	6	2	2	NUM
ejpam-393	318	7	,	,	PUNCT
ejpam-393	318	8	let	let	VERB
ejpam-393	318	9	τ	τ	PRON
ejpam-393	318	10	be	be	AUX
ejpam-393	318	11	a	a	DET
ejpam-393	318	12	partial	partial	ADJ
ejpam-393	318	13	isomorphism	isomorphism	NOUN
ejpam-393	318	14	of	of	ADP
ejpam-393	318	15	nr	nr	PRON
ejpam-393	318	16	and	and	CCONJ
ejpam-393	318	17	let	let	VERB
ejpam-393	318	18	θ	θ	NOUN
ejpam-393	318	19	be	be	AUX
ejpam-393	318	20	any	any	DET
ejpam-393	318	21	finite	finite	ADJ
ejpam-393	318	22	surjection	surjection	NOUN
ejpam-393	318	23	onto	onto	ADP
ejpam-393	318	24	a	a	DET
ejpam-393	318	25	partial	partial	ADJ
ejpam-393	318	26	isomorphism	isomorphism	NOUN
ejpam-393	318	27	of	of	ADP
ejpam-393	318	28	nr	nr	PRON
ejpam-393	318	29	such	such	ADJ
ejpam-393	318	30	that	that	PRON
ejpam-393	318	31	dom(θ	dom(θ	PROPN
ejpam-393	318	32	)	)	PUNCT
ejpam-393	318	33	∩	∩	ADJ
ejpam-393	318	34	nodes(nr	nodes(nr	ADJ
ejpam-393	318	35	)	)	PUNCT
ejpam-393	318	36	=	=	SYM
ejpam-393	318	37	domτ	domτ	PROPN
ejpam-393	318	38	.	.	PUNCT
ejpam-393	319	1	∃	∃	PROPN
ejpam-393	319	2	’s	’s	PART
ejpam-393	319	3	response	response	NOUN
ejpam-393	319	4	to	to	ADP
ejpam-393	319	5	∀	∀	NOUN
ejpam-393	319	6	’s	’s	PART
ejpam-393	319	7	move	move	NOUN
ejpam-393	319	8	(	(	PUNCT
ejpam-393	319	9	nr	nr	INTJ
ejpam-393	319	10	,	,	PUNCT
ejpam-393	319	11	θ	θ	PROPN
ejpam-393	319	12	)	)	PUNCT
ejpam-393	319	13	is	be	AUX
ejpam-393	319	14	necessarily	necessarily	ADV
ejpam-393	319	15	nθ	nθ	ADJ
ejpam-393	319	16	.	.	PUNCT
ejpam-393	320	1	let	let	VERB
ejpam-393	320	2	nr+1	nr+1	PRON
ejpam-393	320	3	be	be	AUX
ejpam-393	320	4	her	her	PRON
ejpam-393	320	5	response	response	NOUN
ejpam-393	320	6	,	,	PUNCT
ejpam-393	320	7	using	use	VERB
ejpam-393	320	8	her	her	PRON
ejpam-393	320	9	wining	wining	NOUN
ejpam-393	320	10	strategy	strategy	NOUN
ejpam-393	320	11	,	,	PUNCT
ejpam-393	320	12	to	to	ADP
ejpam-393	320	13	the	the	DET
ejpam-393	320	14	subsequent	subsequent	ADJ
ejpam-393	320	15	∀move	∀move	NOUN
ejpam-393	320	16	(	(	PUNCT
ejpam-393	320	17	nr	nr	INTJ
ejpam-393	320	18	,	,	PUNCT
ejpam-393	320	19	nrθ	nrθ	ADJ
ejpam-393	320	20	)	)	PUNCT
ejpam-393	320	21	.	.	PUNCT
ejpam-393	321	1	now	now	ADV
ejpam-393	321	2	let	let	VERB
ejpam-393	321	3	na	na	PART
ejpam-393	321	4	be	be	AUX
ejpam-393	321	5	the	the	DET
ejpam-393	321	6	limit	limit	NOUN
ejpam-393	321	7	of	of	ADP
ejpam-393	321	8	this	this	DET
ejpam-393	321	9	sequence	sequence	NOUN
ejpam-393	321	10	.	.	PUNCT
ejpam-393	322	1	this	this	DET
ejpam-393	322	2	limit	limit	NOUN
ejpam-393	322	3	is	be	AUX
ejpam-393	322	4	well	well	ADV
ejpam-393	322	5	-	-	PUNCT
ejpam-393	322	6	defined	define	VERB
ejpam-393	322	7	since	since	SCONJ
ejpam-393	322	8	the	the	DET
ejpam-393	322	9	hypernetworks	hypernetwork	NOUN
ejpam-393	322	10	are	be	AUX
ejpam-393	322	11	nested	nest	VERB
ejpam-393	322	12	.	.	PUNCT
ejpam-393	323	1	note	note	NOUN
ejpam-393	323	2	,	,	PUNCT
ejpam-393	323	3	for	for	ADP
ejpam-393	323	4	b	b	PROPN
ejpam-393	323	5	∈	∈	PROPN
ejpam-393	323	6	α	α	NOUN
ejpam-393	323	7	,	,	PUNCT
ejpam-393	323	8	that	that	SCONJ
ejpam-393	323	9	(	(	PUNCT
ejpam-393	323	10	∃i0	∃i0	PROPN
ejpam-393	323	11	,	,	PUNCT
ejpam-393	323	12	.	.	PUNCT
ejpam-393	323	13	.	.	PUNCT
ejpam-393	323	14	.	.	PUNCT
ejpam-393	324	1	iµ−1	iµ−1	NOUN
ejpam-393	324	2	∈	∈	PROPN
ejpam-393	324	3	nodes(na	nodes(na	NOUN
ejpam-393	324	4	)	)	PUNCT
ejpam-393	324	5	,	,	PUNCT
ejpam-393	324	6	na(i0	na(i0	PROPN
ejpam-393	324	7	.	.	PUNCT
ejpam-393	324	8	.	.	PUNCT
ejpam-393	324	9	.	.	PUNCT
ejpam-393	325	1	,	,	PUNCT
ejpam-393	325	2	iµ−1	iµ−1	NOUN
ejpam-393	325	3	)	)	PUNCT
ejpam-393	326	1	=	=	SYM
ejpam-393	326	2	b	b	X
ejpam-393	326	3	)	)	PUNCT
ejpam-393	326	4	⇐	⇐	ADJ
ejpam-393	326	5	⇒	⇒	NOUN
ejpam-393	326	6	b	b	NOUN
ejpam-393	326	7	∼	∼	NOUN
ejpam-393	326	8	a	a	DET
ejpam-393	326	9	(	(	PUNCT
ejpam-393	326	10	1	1	NUM
ejpam-393	326	11	)	)	PUNCT
ejpam-393	326	12	let	let	VERB
ejpam-393	326	13	θ	θ	NOUN
ejpam-393	326	14	be	be	AUX
ejpam-393	326	15	any	any	DET
ejpam-393	326	16	finite	finite	ADJ
ejpam-393	326	17	partial	partial	ADJ
ejpam-393	326	18	isomorphism	isomorphism	NOUN
ejpam-393	326	19	of	of	ADP
ejpam-393	326	20	na	na	PUNCT
ejpam-393	326	21	and	and	CCONJ
ejpam-393	326	22	let	let	VERB
ejpam-393	326	23	x	x	PRON
ejpam-393	326	24	be	be	AUX
ejpam-393	326	25	any	any	DET
ejpam-393	326	26	finite	finite	NOUN
ejpam-393	326	27	subset	subset	NOUN
ejpam-393	326	28	of	of	ADP
ejpam-393	326	29	nodes(na	nodes(na	NOUN
ejpam-393	326	30	)	)	PUNCT
ejpam-393	326	31	.	.	PUNCT
ejpam-393	327	1	since	since	SCONJ
ejpam-393	327	2	θ	θ	PROPN
ejpam-393	327	3	,	,	PUNCT
ejpam-393	327	4	x	x	PRON
ejpam-393	327	5	are	be	AUX
ejpam-393	327	6	finite	finite	ADJ
ejpam-393	327	7	,	,	PUNCT
ejpam-393	327	8	there	there	PRON
ejpam-393	327	9	is	be	VERB
ejpam-393	327	10	i	i	PRON
ejpam-393	327	11	<	<	X
ejpam-393	327	12	ω	ω	NUM
ejpam-393	327	13	such	such	ADJ
ejpam-393	327	14	that	that	SCONJ
ejpam-393	327	15	nodes(ni	nodes(ni	PROPN
ejpam-393	327	16	)	)	PUNCT
ejpam-393	327	17	⊇	⊇	NOUN
ejpam-393	327	18	x	x	SYM
ejpam-393	327	19	∪	∪	ADP
ejpam-393	327	20	dom(θ	dom(θ	NOUN
ejpam-393	327	21	)	)	PUNCT
ejpam-393	327	22	.	.	PUNCT
ejpam-393	328	1	there	there	PRON
ejpam-393	328	2	is	be	VERB
ejpam-393	328	3	a	a	DET
ejpam-393	328	4	bijection	bijection	NOUN
ejpam-393	328	5	θ+	θ+	PUNCT
ejpam-393	328	6	⊇	⊇	PROPN
ejpam-393	328	7	θ	θ	PROPN
ejpam-393	328	8	onto	onto	ADP
ejpam-393	328	9	nodes(ni	nodes(ni	PROPN
ejpam-393	328	10	)	)	PUNCT
ejpam-393	328	11	and	and	CCONJ
ejpam-393	328	12	j	j	PROPN
ejpam-393	328	13	≥	≥	NUM
ejpam-393	328	14	i	i	PRON
ejpam-393	328	15	such	such	ADJ
ejpam-393	328	16	that	that	SCONJ
ejpam-393	328	17	n	n	PROPN
ejpam-393	328	18	j	j	PROPN
ejpam-393	328	19	⊇	⊇	PROPN
ejpam-393	328	20	ni	ni	PROPN
ejpam-393	328	21	,	,	PUNCT
ejpam-393	328	22	niθ	niθ	X
ejpam-393	328	23	+	+	X
ejpam-393	328	24	.	.	PUNCT
ejpam-393	329	1	then	then	ADV
ejpam-393	329	2	θ+	θ+	VERB
ejpam-393	329	3	is	be	AUX
ejpam-393	329	4	a	a	DET
ejpam-393	329	5	partial	partial	ADJ
ejpam-393	329	6	isomorphism	isomorphism	NOUN
ejpam-393	329	7	of	of	ADP
ejpam-393	329	8	n	n	PROPN
ejpam-393	329	9	j	j	PROPN
ejpam-393	329	10	and	and	CCONJ
ejpam-393	329	11	rng(θ+	rng(θ+	NOUN
ejpam-393	329	12	)	)	PUNCT
ejpam-393	329	13	=	=	SYM
ejpam-393	329	14	nodes(ni	nodes(ni	PROPN
ejpam-393	329	15	)	)	PUNCT
ejpam-393	329	16	⊇	⊇	NOUN
ejpam-393	329	17	x	x	X
ejpam-393	329	18	.	.	PUNCT
ejpam-393	330	1	hence	hence	ADV
ejpam-393	330	2	,	,	PUNCT
ejpam-393	330	3	if	if	SCONJ
ejpam-393	330	4	θ	θ	PROPN
ejpam-393	330	5	is	be	AUX
ejpam-393	330	6	any	any	DET
ejpam-393	330	7	finite	finite	ADJ
ejpam-393	330	8	partial	partial	ADJ
ejpam-393	330	9	isomorphism	isomorphism	NOUN
ejpam-393	330	10	of	of	ADP
ejpam-393	330	11	na	na	NOUN
ejpam-393	330	12	and	and	CCONJ
ejpam-393	330	13	x	x	X
ejpam-393	330	14	is	be	AUX
ejpam-393	330	15	any	any	DET
ejpam-393	330	16	finite	finite	NOUN
ejpam-393	330	17	subset	subset	NOUN
ejpam-393	330	18	of	of	ADP
ejpam-393	330	19	nodes(na	nodes(na	NOUN
ejpam-393	330	20	)	)	PUNCT
ejpam-393	330	21	then	then	ADV
ejpam-393	330	22	∃	∃	PROPN
ejpam-393	330	23	a	a	DET
ejpam-393	330	24	partial	partial	ADJ
ejpam-393	330	25	isomorphism	isomorphism	NOUN
ejpam-393	330	26	θ+	θ+	PUNCT
ejpam-393	330	27	⊇	⊇	PROPN
ejpam-393	330	28	θ	θ	PROPN
ejpam-393	330	29	of	of	ADP
ejpam-393	330	30	na	na	INTJ
ejpam-393	330	31	where	where	SCONJ
ejpam-393	330	32	rng(θ+)⊇	rng(θ+)⊇	PROPN
ejpam-393	330	33	x	x	X
ejpam-393	330	34	(	(	PUNCT
ejpam-393	330	35	2	2	NUM
ejpam-393	330	36	)	)	PUNCT
ejpam-393	330	37	and	and	CCONJ
ejpam-393	330	38	by	by	ADP
ejpam-393	330	39	considering	consider	VERB
ejpam-393	330	40	its	its	PRON
ejpam-393	330	41	inverse	inverse	NOUN
ejpam-393	330	42	we	we	PRON
ejpam-393	330	43	can	can	AUX
ejpam-393	330	44	extend	extend	VERB
ejpam-393	330	45	a	a	DET
ejpam-393	330	46	partial	partial	ADJ
ejpam-393	330	47	isomorphism	isomorphism	NOUN
ejpam-393	330	48	so	so	SCONJ
ejpam-393	330	49	as	as	SCONJ
ejpam-393	330	50	to	to	PART
ejpam-393	330	51	include	include	VERB
ejpam-393	330	52	an	an	DET
ejpam-393	330	53	arbitrary	arbitrary	ADJ
ejpam-393	330	54	finite	finite	NOUN
ejpam-393	330	55	subset	subset	NOUN
ejpam-393	330	56	of	of	ADP
ejpam-393	330	57	nodes(na	nodes(na	NOUN
ejpam-393	330	58	)	)	PUNCT
ejpam-393	330	59	within	within	ADP
ejpam-393	330	60	its	its	PRON
ejpam-393	330	61	domain	domain	NOUN
ejpam-393	330	62	.	.	PUNCT
ejpam-393	331	1	let	let	VERB
ejpam-393	331	2	l	l	NOUN
ejpam-393	331	3	be	be	AUX
ejpam-393	331	4	the	the	DET
ejpam-393	331	5	signature	signature	NOUN
ejpam-393	331	6	with	with	ADP
ejpam-393	331	7	one	one	NUM
ejpam-393	331	8	µ	µ	PRON
ejpam-393	331	9	-ary	-ary	ADJ
ejpam-393	331	10	predicate	predicate	NOUN
ejpam-393	331	11	symbol	symbol	NOUN
ejpam-393	331	12	(	(	PUNCT
ejpam-393	331	13	b	b	NOUN
ejpam-393	331	14	)	)	PUNCT
ejpam-393	331	15	for	for	ADP
ejpam-393	331	16	each	each	DET
ejpam-393	331	17	b	b	PROPN
ejpam-393	331	18	∈	∈	PROPN
ejpam-393	331	19	α	α	NOUN
ejpam-393	331	20	,	,	PUNCT
ejpam-393	331	21	and	and	CCONJ
ejpam-393	331	22	one	one	NUM
ejpam-393	331	23	k	k	ADJ
ejpam-393	331	24	-	-	ADJ
ejpam-393	331	25	ary	ary	ADJ
ejpam-393	331	26	predicate	predicate	NOUN
ejpam-393	331	27	symbol	symbol	NOUN
ejpam-393	331	28	(	(	PUNCT
ejpam-393	331	29	λ	λ	NOUN
ejpam-393	331	30	)	)	PUNCT
ejpam-393	331	31	for	for	ADP
ejpam-393	331	32	each	each	DET
ejpam-393	331	33	k	k	ADJ
ejpam-393	331	34	-	-	PROPN
ejpam-393	331	35	ary	ary	PROPN
ejpam-393	331	36	hyperlabel	hyperlabel	PROPN
ejpam-393	331	37	λ	λ	PROPN
ejpam-393	331	38	.	.	PUNCT
ejpam-393	332	1	[	[	X
ejpam-393	332	2	notational	notational	ADJ
ejpam-393	332	3	point	point	NOUN
ejpam-393	332	4	:	:	PUNCT
ejpam-393	332	5	if	if	SCONJ
ejpam-393	332	6	λ	λ	PROPN
ejpam-393	332	7	is	be	AUX
ejpam-393	332	8	k	k	NOUN
ejpam-393	332	9	-	-	ADJ
ejpam-393	332	10	ary	ary	PROPN
ejpam-393	332	11	and	and	CCONJ
ejpam-393	332	12	l	l	NOUN
ejpam-393	332	13	-	-	NOUN
ejpam-393	332	14	ary	ary	PROPN
ejpam-393	332	15	for	for	ADP
ejpam-393	332	16	k	k	PROPN
ejpam-393	332	17	6=	6=	PROPN
ejpam-393	332	18	l	l	PROPN
ejpam-393	332	19	then	then	ADV
ejpam-393	332	20	make	make	VERB
ejpam-393	332	21	one	one	NUM
ejpam-393	332	22	k	k	ADJ
ejpam-393	332	23	-	-	ADJ
ejpam-393	332	24	ary	ary	ADJ
ejpam-393	332	25	predicate	predicate	NOUN
ejpam-393	332	26	symbol	symbol	NOUN
ejpam-393	332	27	λ	λ	PROPN
ejpam-393	332	28	and	and	CCONJ
ejpam-393	332	29	one	one	NUM
ejpam-393	332	30	l	l	ADJ
ejpam-393	332	31	-	-	ADJ
ejpam-393	332	32	ary	ary	ADJ
ejpam-393	332	33	predicate	predicate	ADJ
ejpam-393	332	34	symbol	symbol	NOUN
ejpam-393	332	35	λ′	λ′	NOUN
ejpam-393	332	36	,	,	PUNCT
ejpam-393	332	37	so	so	SCONJ
ejpam-393	332	38	that	that	SCONJ
ejpam-393	332	39	every	every	DET
ejpam-393	332	40	predicate	predicate	NOUN
ejpam-393	332	41	symbol	symbol	NOUN
ejpam-393	332	42	has	have	VERB
ejpam-393	332	43	a	a	DET
ejpam-393	332	44	unique	unique	ADJ
ejpam-393	332	45	arity	arity	NOUN
ejpam-393	332	46	.	.	PUNCT
ejpam-393	332	47	]	]	PUNCT
ejpam-393	333	1	the	the	DET
ejpam-393	333	2	set	set	NOUN
ejpam-393	333	3	of	of	ADP
ejpam-393	333	4	variables	variable	NOUN
ejpam-393	333	5	for	for	ADP
ejpam-393	333	6	l	l	NOUN
ejpam-393	333	7	-	-	NOUN
ejpam-393	333	8	formulas	formula	NOUN
ejpam-393	333	9	is	be	AUX
ejpam-393	333	10	{	{	PUNCT
ejpam-393	333	11	x	x	PROPN
ejpam-393	333	12	i	i	NOUN
ejpam-393	333	13	:	:	PUNCT
ejpam-393	334	1	i	i	PRON
ejpam-393	334	2	<	<	X
ejpam-393	334	3	ω	ω	X
ejpam-393	334	4	}	}	PUNCT
ejpam-393	334	5	.	.	PUNCT
ejpam-393	335	1	we	we	PRON
ejpam-393	335	2	also	also	ADV
ejpam-393	335	3	have	have	VERB
ejpam-393	335	4	equality	equality	NOUN
ejpam-393	335	5	.	.	PUNCT
ejpam-393	336	1	pick	pick	VERB
ejpam-393	336	2	fa	fa	PROPN
ejpam-393	336	3	∈	∈	PROPN
ejpam-393	336	4	ωnodes(na	ωnodes(na	PROPN
ejpam-393	336	5	)	)	PUNCT
ejpam-393	336	6	.	.	PUNCT
ejpam-393	337	1	let	let	VERB
ejpam-393	337	2	ua	ua	PROPN
ejpam-393	337	3	=	=	PRON
ejpam-393	337	4	{	{	PUNCT
ejpam-393	337	5	f	f	PROPN
ejpam-393	337	6	∈	∈	PROPN
ejpam-393	337	7	ωnodes(na	ωnodes(na	PROPN
ejpam-393	337	8	)	)	PUNCT
ejpam-393	337	9	:	:	PUNCT
ejpam-393	337	10	{	{	PUNCT
ejpam-393	337	11	i	i	PRON
ejpam-393	337	12	<	<	X
ejpam-393	337	13	ω	ω	X
ejpam-393	337	14	:	:	PUNCT
ejpam-393	337	15	g(i	g(i	PROPN
ejpam-393	337	16	)	)	PUNCT
ejpam-393	337	17	6=	6=	NUM
ejpam-393	337	18	fa(i	fa(i	NOUN
ejpam-393	337	19	)	)	PUNCT
ejpam-393	337	20	}	}	PUNCT
ejpam-393	337	21	is	be	AUX
ejpam-393	337	22	finite	finite	ADJ
ejpam-393	337	23	}	}	PUNCT
ejpam-393	337	24	.	.	PUNCT
ejpam-393	338	1	we	we	PRON
ejpam-393	338	2	can	can	AUX
ejpam-393	338	3	make	make	VERB
ejpam-393	338	4	ua	ua	NOUN
ejpam-393	338	5	into	into	ADP
ejpam-393	338	6	the	the	DET
ejpam-393	338	7	base	base	NOUN
ejpam-393	338	8	of	of	ADP
ejpam-393	338	9	an	an	DET
ejpam-393	338	10	l	l	NOUN
ejpam-393	338	11	-	-	NOUN
ejpam-393	338	12	structure	structure	NOUN
ejpam-393	338	13	na	na	NOUN
ejpam-393	338	14	and	and	CCONJ
ejpam-393	338	15	evaluate	evaluate	VERB
ejpam-393	338	16	l	l	NOUN
ejpam-393	338	17	-	-	NOUN
ejpam-393	338	18	formulas	formula	NOUN
ejpam-393	338	19	at	at	ADP
ejpam-393	338	20	f	f	PROPN
ejpam-393	338	21	∈	∈	PROPN
ejpam-393	338	22	ua	ua	PROPN
ejpam-393	338	23	as	as	SCONJ
ejpam-393	338	24	follow	follow	VERB
ejpam-393	338	25	.	.	PUNCT
ejpam-393	339	1	for	for	ADP
ejpam-393	339	2	b	b	PROPN
ejpam-393	339	3	∈	∈	PROPN
ejpam-393	339	4	α	α	PROPN
ejpam-393	339	5	,	,	PUNCT
ejpam-393	339	6	l0	l0	PROPN
ejpam-393	339	7	,	,	PUNCT
ejpam-393	339	8	.	.	PUNCT
ejpam-393	339	9	.	.	PUNCT
ejpam-393	339	10	.	.	PUNCT
ejpam-393	340	1	lµ−1	lµ−1	PROPN
ejpam-393	340	2	,	,	PUNCT
ejpam-393	340	3	i0	i0	PROPN
ejpam-393	340	4	.	.	PUNCT
ejpam-393	340	5	.	.	PUNCT
ejpam-393	341	1	.	.	PUNCT
ejpam-393	342	1	,	,	PUNCT
ejpam-393	342	2	ik−1	ik−1	PROPN
ejpam-393	342	3	<	<	PROPN
ejpam-393	342	4	ω	ω	PROPN
ejpam-393	342	5	,	,	PUNCT
ejpam-393	342	6	k	k	ADJ
ejpam-393	342	7	-	-	ADJ
ejpam-393	342	8	ary	ary	PROPN
ejpam-393	342	9	hyperlabels	hyperlabels	PROPN
ejpam-393	342	10	λ	λ	PROPN
ejpam-393	342	11	,	,	PUNCT
ejpam-393	342	12	and	and	CCONJ
ejpam-393	342	13	all	all	DET
ejpam-393	342	14	l	l	NOUN
ejpam-393	342	15	-	-	NOUN
ejpam-393	342	16	formulas	formulas	ADJ
ejpam-393	342	17	φ	φ	NOUN
ejpam-393	342	18	,	,	PUNCT
ejpam-393	342	19	ψ	ψ	ADP
ejpam-393	342	20	,	,	PUNCT
ejpam-393	342	21	let	let	VERB
ejpam-393	342	22	na	na	PART
ejpam-393	342	23	,	,	PUNCT
ejpam-393	342	24	f	f	X
ejpam-393	342	25	|=	|=	PUNCT
ejpam-393	342	26	b(x	b(x	NOUN
ejpam-393	342	27	l0	l0	PROPN
ejpam-393	342	28	.	.	PUNCT
ejpam-393	342	29	.	.	PUNCT
ejpam-393	342	30	.	.	PUNCT
ejpam-393	343	1	xn−1	xn−1	PROPN
ejpam-393	343	2	)	)	PUNCT
ejpam-393	344	1	⇐	⇐	ADJ
ejpam-393	344	2	⇒	⇒	NOUN
ejpam-393	344	3	na	na	PROPN
ejpam-393	344	4	(	(	PUNCT
ejpam-393	344	5	f	f	PROPN
ejpam-393	344	6	(	(	PUNCT
ejpam-393	344	7	l0	l0	PROPN
ejpam-393	344	8	)	)	PUNCT
ejpam-393	344	9	,	,	PUNCT
ejpam-393	344	10	.	.	PUNCT
ejpam-393	344	11	.	.	PUNCT
ejpam-393	344	12	.	.	PUNCT
ejpam-393	345	1	f	f	PROPN
ejpam-393	345	2	(	(	PUNCT
ejpam-393	345	3	ln−1	ln−1	PROPN
ejpam-393	345	4	)	)	PUNCT
ejpam-393	345	5	)	)	PUNCT
ejpam-393	346	1	=	=	SYM
ejpam-393	346	2	b	b	X
ejpam-393	346	3	na	na	NOUN
ejpam-393	346	4	,	,	PUNCT
ejpam-393	346	5	f	f	PROPN
ejpam-393	346	6	|=	|=	PUNCT
ejpam-393	346	7	λ(x	λ(x	PROPN
ejpam-393	346	8	i0	i0	PROPN
ejpam-393	346	9	,	,	PUNCT
ejpam-393	346	10	.	.	PUNCT
ejpam-393	346	11	.	.	PUNCT
ejpam-393	346	12	.	.	PUNCT
ejpam-393	347	1	,	,	PUNCT
ejpam-393	347	2	x	x	PUNCT
ejpam-393	347	3	ik−1	ik−1	PROPN
ejpam-393	347	4	)	)	PUNCT
ejpam-393	347	5	⇐	⇐	ADJ
ejpam-393	347	6	⇒	⇒	NOUN
ejpam-393	347	7	na	na	PROPN
ejpam-393	347	8	(	(	PUNCT
ejpam-393	347	9	f	f	PROPN
ejpam-393	347	10	(	(	PUNCT
ejpam-393	347	11	i0	i0	PROPN
ejpam-393	347	12	)	)	PUNCT
ejpam-393	347	13	,	,	PUNCT
ejpam-393	347	14	.	.	PUNCT
ejpam-393	347	15	.	.	PUNCT
ejpam-393	348	1	.	.	PUNCT
ejpam-393	349	1	,	,	PUNCT
ejpam-393	349	2	f	f	PROPN
ejpam-393	349	3	(	(	PUNCT
ejpam-393	349	4	ik−1	ik−1	PROPN
ejpam-393	349	5	)	)	PUNCT
ejpam-393	349	6	)	)	PUNCT
ejpam-393	350	1	=	=	PUNCT
ejpam-393	350	2	λ	λ	X
ejpam-393	350	3	na	na	NOUN
ejpam-393	350	4	,	,	PUNCT
ejpam-393	350	5	f	f	PROPN
ejpam-393	350	6	|=	|=	PUNCT
ejpam-393	350	7	¬φ	¬φ	VERB
ejpam-393	350	8	⇐	⇐	ADJ
ejpam-393	350	9	⇒	⇒	NOUN
ejpam-393	350	10	na	na	ADP
ejpam-393	350	11	,	,	PUNCT
ejpam-393	350	12	f	f	PROPN
ejpam-393	350	13	6|=	6|=	NUM
ejpam-393	350	14	φ	φ	PROPN
ejpam-393	350	15	na	na	PROPN
ejpam-393	350	16	,	,	PUNCT
ejpam-393	350	17	f	f	PROPN
ejpam-393	350	18	|=	|=	X
ejpam-393	350	19	(	(	PUNCT
ejpam-393	350	20	φ	φ	PROPN
ejpam-393	350	21	∨ψ	∨ψ	PROPN
ejpam-393	350	22	)	)	PUNCT
ejpam-393	350	23	⇐	⇐	ADJ
ejpam-393	350	24	⇒	⇒	NOUN
ejpam-393	350	25	na	na	ADP
ejpam-393	350	26	,	,	PUNCT
ejpam-393	350	27	f	f	PROPN
ejpam-393	350	28	|=	|=	PUNCT
ejpam-393	350	29	φ	φ	NOUN
ejpam-393	350	30	or	or	CCONJ
ejpam-393	350	31	na	na	ADP
ejpam-393	350	32	,	,	PUNCT
ejpam-393	350	33	f	f	PROPN
ejpam-393	350	34	|=ψ	|=ψ	NUM
ejpam-393	350	35	na	na	PROPN
ejpam-393	350	36	,	,	PUNCT
ejpam-393	350	37	f	f	PROPN
ejpam-393	350	38	|=	|=	PUNCT
ejpam-393	351	1	∃x	∃x	ADV
ejpam-393	351	2	iφ	iφ	VERB
ejpam-393	351	3	⇐	⇐	ADJ
ejpam-393	351	4	⇒	⇒	NOUN
ejpam-393	351	5	na	na	ADP
ejpam-393	351	6	,	,	PUNCT
ejpam-393	351	7	f	f	PROPN
ejpam-393	352	1	[	[	X
ejpam-393	352	2	i	i	X
ejpam-393	352	3	/	/	SYM
ejpam-393	352	4	m	m	VERB
ejpam-393	352	5	]	]	X
ejpam-393	352	6	|=	|=	PUNCT
ejpam-393	352	7	φ	φ	NUM
ejpam-393	352	8	,	,	PUNCT
ejpam-393	352	9	some	some	DET
ejpam-393	352	10	m	m	NOUN
ejpam-393	352	11	∈	∈	NOUN
ejpam-393	352	12	nodes(na	nodes(na	NOUN
ejpam-393	352	13	)	)	PUNCT
ejpam-393	352	14	for	for	ADP
ejpam-393	352	15	any	any	DET
ejpam-393	352	16	l	l	NOUN
ejpam-393	352	17	-	-	NOUN
ejpam-393	352	18	formula	formula	NOUN
ejpam-393	352	19	φ	φ	NOUN
ejpam-393	352	20	,	,	PUNCT
ejpam-393	352	21	write	write	VERB
ejpam-393	352	22	φna	φna	NOUN
ejpam-393	352	23	for	for	ADP
ejpam-393	352	24	{	{	PUNCT
ejpam-393	352	25	f	f	PROPN
ejpam-393	352	26	∈	∈	PROPN
ejpam-393	352	27	ωnodes(na	ωnodes(na	PROPN
ejpam-393	352	28	)	)	PUNCT
ejpam-393	352	29	:	:	PUNCT
ejpam-393	353	1	na	na	X
ejpam-393	353	2	,	,	PUNCT
ejpam-393	353	3	f	f	PROPN
ejpam-393	353	4	|=	|=	X
ejpam-393	353	5	φ	φ	NUM
ejpam-393	353	6	}	}	PUNCT
ejpam-393	353	7	.	.	PUNCT
ejpam-393	354	1	let	let	VERB
ejpam-393	354	2	formna	formna	VERB
ejpam-393	354	3	=	=	SYM
ejpam-393	354	4	{	{	PUNCT
ejpam-393	354	5	φna	φna	NOUN
ejpam-393	354	6	:	:	PUNCT
ejpam-393	354	7	φ	φ	PROPN
ejpam-393	354	8	is	be	AUX
ejpam-393	354	9	an	an	DET
ejpam-393	354	10	l	l	NOUN
ejpam-393	354	11	-	-	NOUN
ejpam-393	354	12	formula	formula	NOUN
ejpam-393	354	13	}	}	PUNCT
ejpam-393	354	14	and	and	CCONJ
ejpam-393	354	15	define	define	VERB
ejpam-393	354	16	a	a	DET
ejpam-393	354	17	cylindric	cylindric	ADJ
ejpam-393	354	18	algebra	algebra	NOUN
ejpam-393	354	19	da	da	NOUN
ejpam-393	354	20	=	=	PUNCT
ejpam-393	354	21	(	(	PUNCT
ejpam-393	354	22	formna	formna	VERB
ejpam-393	354	23	,	,	PUNCT
ejpam-393	354	24	∪,∼,di	∪,∼,di	PROPN
ejpam-393	354	25	j	j	PROPN
ejpam-393	354	26	,	,	PUNCT
ejpam-393	354	27	ci	ci	PROPN
ejpam-393	354	28	,	,	PUNCT
ejpam-393	354	29	i	i	PRON
ejpam-393	354	30	,	,	PUNCT
ejpam-393	354	31	j	j	PROPN
ejpam-393	354	32	<	<	X
ejpam-393	354	33	ω	ω	PROPN
ejpam-393	354	34	)	)	PUNCT
ejpam-393	354	35	where	where	SCONJ
ejpam-393	354	36	di	di	X
ejpam-393	354	37	j	j	PROPN
ejpam-393	354	38	=	=	PUNCT
ejpam-393	354	39	(	(	PUNCT
ejpam-393	354	40	x	x	X
ejpam-393	354	41	i	i	NOUN
ejpam-393	354	42	=	=	NOUN
ejpam-393	354	43	x	x	SYM
ejpam-393	354	44	j	j	PROPN
ejpam-393	354	45	)	)	PUNCT
ejpam-393	354	46	na	na	NOUN
ejpam-393	354	47	,	,	PUNCT
ejpam-393	354	48	ci(φ	ci(φ	NOUN
ejpam-393	354	49	na	na	NOUN
ejpam-393	354	50	)	)	PUNCT
ejpam-393	355	1	=	=	SYM
ejpam-393	355	2	(	(	PUNCT
ejpam-393	355	3	∃x	∃x	NOUN
ejpam-393	355	4	iφ	iφ	NOUN
ejpam-393	355	5	)	)	PUNCT
ejpam-393	355	6	na	na	NOUN
ejpam-393	355	7	.	.	PUNCT
ejpam-393	356	1	observe	observe	VERB
ejpam-393	356	2	that	that	SCONJ
ejpam-393	356	3	⊤na	⊤na	NOUN
ejpam-393	356	4	=	=	SYM
ejpam-393	356	5	ua	ua	PROPN
ejpam-393	356	6	,	,	PUNCT
ejpam-393	356	7	(	(	PUNCT
ejpam-393	356	8	φ	φ	X
ejpam-393	356	9	∨	∨	NUM
ejpam-393	356	10	ψ)na	ψ)na	PROPN
ejpam-393	356	11	=	=	PUNCT
ejpam-393	356	12	φna	φna	PROPN
ejpam-393	356	13	∪ψna	∪ψna	PROPN
ejpam-393	356	14	,	,	PUNCT
ejpam-393	356	15	etc	etc	X
ejpam-393	356	16	.	.	X
ejpam-393	357	1	note	note	VERB
ejpam-393	357	2	also	also	ADV
ejpam-393	357	3	that	that	SCONJ
ejpam-393	357	4	d	d	NOUN
ejpam-393	357	5	is	be	AUX
ejpam-393	357	6	a	a	DET
ejpam-393	357	7	subalgebra	subalgebra	NOUN
ejpam-393	357	8	of	of	ADP
ejpam-393	357	9	the	the	DET
ejpam-393	357	10	ω	ω	ADJ
ejpam-393	357	11	-	-	ADJ
ejpam-393	357	12	dimensional	dimensional	ADJ
ejpam-393	357	13	cylindric	cylindric	ADJ
ejpam-393	357	14	set	set	NOUN
ejpam-393	357	15	algebra	algebra	NOUN
ejpam-393	357	16	on	on	ADP
ejpam-393	357	17	the	the	DET
ejpam-393	357	18	base	base	NOUN
ejpam-393	357	19	nodes(na	nodes(na	NOUN
ejpam-393	357	20	)	)	PUNCT
ejpam-393	357	21	,	,	PUNCT
ejpam-393	357	22	hence	hence	ADV
ejpam-393	357	23	d	d	PROPN
ejpam-393	357	24	∈	∈	PROPN
ejpam-393	357	25	rcaω	rcaω	PROPN
ejpam-393	357	26	.	.	PUNCT
ejpam-393	358	1	t.	t.	PROPN
ejpam-393	358	2	ahmed	ahmed	PROPN
ejpam-393	358	3	/	/	SYM
ejpam-393	358	4	eur	eur	PROPN
ejpam-393	358	5	.	.	PUNCT
ejpam-393	359	1	j.	j.	PROPN
ejpam-393	359	2	pure	pure	PROPN
ejpam-393	359	3	appl	appl	PROPN
ejpam-393	359	4	.	.	PROPN
ejpam-393	359	5	math	math	PROPN
ejpam-393	359	6	,	,	PUNCT
ejpam-393	359	7	3	3	NUM
ejpam-393	359	8	(	(	PUNCT
ejpam-393	359	9	2010	2010	NUM
ejpam-393	359	10	)	)	PUNCT
ejpam-393	359	11	,	,	PUNCT
ejpam-393	359	12	853	853	NUM
ejpam-393	359	13	-	-	SYM
ejpam-393	359	14	880	880	NUM
ejpam-393	359	15	861	861	NUM
ejpam-393	359	16	let	let	VERB
ejpam-393	359	17	φ(x	φ(x	PROPN
ejpam-393	359	18	i0	i0	PROPN
ejpam-393	359	19	,	,	PUNCT
ejpam-393	359	20	x	x	PROPN
ejpam-393	359	21	i1	i1	PROPN
ejpam-393	359	22	,	,	PUNCT
ejpam-393	359	23	.	.	PUNCT
ejpam-393	359	24	.	.	PUNCT
ejpam-393	359	25	.	.	PUNCT
ejpam-393	360	1	,	,	PUNCT
ejpam-393	360	2	x	x	X
ejpam-393	360	3	ik	ik	X
ejpam-393	360	4	)	)	PUNCT
ejpam-393	360	5	be	be	AUX
ejpam-393	360	6	an	an	DET
ejpam-393	360	7	arbitrary	arbitrary	ADJ
ejpam-393	360	8	l	l	NOUN
ejpam-393	360	9	-	-	NOUN
ejpam-393	360	10	formula	formula	NOUN
ejpam-393	360	11	using	use	VERB
ejpam-393	360	12	only	only	ADV
ejpam-393	360	13	variables	variable	NOUN
ejpam-393	360	14	belonging	belong	VERB
ejpam-393	360	15	to	to	ADP
ejpam-393	360	16	{	{	PUNCT
ejpam-393	360	17	x	x	PROPN
ejpam-393	360	18	i0	i0	PROPN
ejpam-393	360	19	,	,	PUNCT
ejpam-393	360	20	.	.	PUNCT
ejpam-393	360	21	.	.	PUNCT
ejpam-393	361	1	.	.	PUNCT
ejpam-393	362	1	,	,	PUNCT
ejpam-393	362	2	x	x	X
ejpam-393	362	3	ik	ik	PROPN
ejpam-393	362	4	}	}	PUNCT
ejpam-393	362	5	.	.	PUNCT
ejpam-393	363	1	let	let	VERB
ejpam-393	363	2	f	f	NOUN
ejpam-393	363	3	,	,	PUNCT
ejpam-393	363	4	g	g	PROPN
ejpam-393	363	5	∈	∈	PROPN
ejpam-393	363	6	ua	ua	PROPN
ejpam-393	363	7	(	(	PUNCT
ejpam-393	363	8	some	some	PRON
ejpam-393	363	9	a	a	DET
ejpam-393	363	10	∈	∈	PROPN
ejpam-393	363	11	α	α	NOUN
ejpam-393	363	12	)	)	PUNCT
ejpam-393	363	13	and	and	CCONJ
ejpam-393	363	14	suppose	suppose	VERB
ejpam-393	363	15	is	be	AUX
ejpam-393	363	16	a	a	DET
ejpam-393	363	17	partial	partial	ADJ
ejpam-393	363	18	isomorphism	isomorphism	NOUN
ejpam-393	363	19	of	of	ADP
ejpam-393	363	20	na	na	PROPN
ejpam-393	363	21	.	.	PUNCT
ejpam-393	364	1	we	we	PRON
ejpam-393	364	2	can	can	AUX
ejpam-393	364	3	prove	prove	VERB
ejpam-393	364	4	by	by	ADP
ejpam-393	364	5	induction	induction	NOUN
ejpam-393	364	6	over	over	ADP
ejpam-393	364	7	the	the	DET
ejpam-393	364	8	quantifier	quantifier	NOUN
ejpam-393	364	9	depth	depth	NOUN
ejpam-393	364	10	of	of	ADP
ejpam-393	364	11	φ	φ	PROPN
ejpam-393	364	12	and	and	CCONJ
ejpam-393	364	13	using	use	VERB
ejpam-393	364	14	(	(	PUNCT
ejpam-393	364	15	2	2	NUM
ejpam-393	364	16	)	)	PUNCT
ejpam-393	364	17	,	,	PUNCT
ejpam-393	364	18	that	that	SCONJ
ejpam-393	364	19	na	na	NOUN
ejpam-393	364	20	,	,	PUNCT
ejpam-393	364	21	f	f	PROPN
ejpam-393	364	22	|=	|=	PROPN
ejpam-393	364	23	φ	φ	X
ejpam-393	364	24	⇐	⇐	PROPN
ejpam-393	364	25	⇒	⇒	PROPN
ejpam-393	364	26	na	na	AUX
ejpam-393	364	27	,	,	PUNCT
ejpam-393	364	28	g	g	PROPN
ejpam-393	364	29	|=	|=	PUNCT
ejpam-393	364	30	φ	φ	X
ejpam-393	364	31	(	(	PUNCT
ejpam-393	364	32	3	3	NUM
ejpam-393	364	33	)	)	PUNCT
ejpam-393	364	34	let	let	VERB
ejpam-393	364	35	c	c	NOUN
ejpam-393	364	36	=	=	SYM
ejpam-393	364	37	∏	∏	PROPN
ejpam-393	364	38	a∈α	a∈α	ADJ
ejpam-393	364	39	da	da	NOUN
ejpam-393	364	40	.	.	PUNCT
ejpam-393	365	1	then	then	ADV
ejpam-393	365	2	c	c	PROPN
ejpam-393	365	3	∈	∈	PROPN
ejpam-393	365	4	rcaω	rcaω	PROPN
ejpam-393	365	5	.	.	PUNCT
ejpam-393	366	1	an	an	DET
ejpam-393	366	2	element	element	NOUN
ejpam-393	366	3	x	x	PUNCT
ejpam-393	366	4	of	of	ADP
ejpam-393	366	5	c	c	PROPN
ejpam-393	366	6	has	have	VERB
ejpam-393	366	7	the	the	DET
ejpam-393	366	8	form	form	NOUN
ejpam-393	366	9	(	(	PUNCT
ejpam-393	366	10	xa	xa	PROPN
ejpam-393	366	11	:	:	PUNCT
ejpam-393	366	12	a	a	DET
ejpam-393	366	13	∈	∈	PROPN
ejpam-393	366	14	α	α	NOUN
ejpam-393	366	15	)	)	PUNCT
ejpam-393	366	16	,	,	PUNCT
ejpam-393	366	17	where	where	SCONJ
ejpam-393	366	18	xa	xa	PROPN
ejpam-393	366	19	∈	∈	PROPN
ejpam-393	366	20	da	da	PROPN
ejpam-393	366	21	.	.	PUNCT
ejpam-393	367	1	for	for	ADP
ejpam-393	367	2	b	b	PROPN
ejpam-393	367	3	∈	∈	PROPN
ejpam-393	367	4	α	α	NOUN
ejpam-393	367	5	let	let	VERB
ejpam-393	367	6	πb	πb	INTJ
ejpam-393	367	7	:	:	PUNCT
ejpam-393	367	8	c	c	X
ejpam-393	367	9	→	→	SYM
ejpam-393	367	10	db	db	PART
ejpam-393	367	11	be	be	AUX
ejpam-393	367	12	the	the	DET
ejpam-393	367	13	projection	projection	NOUN
ejpam-393	367	14	defined	define	VERB
ejpam-393	367	15	by	by	ADP
ejpam-393	367	16	πb(xa	πb(xa	NOUN
ejpam-393	367	17	:	:	PUNCT
ejpam-393	367	18	a	a	DET
ejpam-393	367	19	∈	∈	PROPN
ejpam-393	367	20	α	α	NOUN
ejpam-393	367	21	)	)	PUNCT
ejpam-393	367	22	=	=	SYM
ejpam-393	367	23	xb	xb	PROPN
ejpam-393	367	24	.	.	PUNCT
ejpam-393	368	1	conversely	conversely	ADV
ejpam-393	368	2	,	,	PUNCT
ejpam-393	368	3	let	let	VERB
ejpam-393	368	4	ιa	ιa	NOUN
ejpam-393	368	5	:	:	PUNCT
ejpam-393	368	6	da	da	X
ejpam-393	368	7	→c	→c	PUNCT
ejpam-393	368	8	be	be	AUX
ejpam-393	368	9	the	the	DET
ejpam-393	368	10	embedding	embed	VERB
ejpam-393	368	11	defined	define	VERB
ejpam-393	368	12	by	by	ADP
ejpam-393	368	13	ιa(y	ιa(y	NOUN
ejpam-393	368	14	)	)	PUNCT
ejpam-393	368	15	=	=	PUNCT
ejpam-393	369	1	(	(	PUNCT
ejpam-393	369	2	xb	xb	X
ejpam-393	369	3	:	:	PUNCT
ejpam-393	369	4	b	b	X
ejpam-393	369	5	∈	∈	PROPN
ejpam-393	369	6	α	α	NOUN
ejpam-393	369	7	)	)	PUNCT
ejpam-393	369	8	,	,	PUNCT
ejpam-393	369	9	where	where	SCONJ
ejpam-393	369	10	xa	xa	PROPN
ejpam-393	369	11	=	=	SYM
ejpam-393	369	12	y	y	PROPN
ejpam-393	369	13	and	and	CCONJ
ejpam-393	369	14	xb	xb	X
ejpam-393	370	1	=	=	NOUN
ejpam-393	370	2	0	0	PROPN
ejpam-393	370	3	for	for	ADP
ejpam-393	370	4	b	b	PROPN
ejpam-393	370	5	6=	6=	ADP
ejpam-393	370	6	a.	a.	NOUN
ejpam-393	370	7	evidently	evidently	ADV
ejpam-393	370	8	πb(ιb(y	πb(ιb(y	ADV
ejpam-393	370	9	)	)	PUNCT
ejpam-393	370	10	)	)	PUNCT
ejpam-393	371	1	=	=	PUNCT
ejpam-393	371	2	y	y	PROPN
ejpam-393	371	3	for	for	ADP
ejpam-393	371	4	y	y	PROPN
ejpam-393	371	5	∈	∈	PROPN
ejpam-393	371	6	db	db	PROPN
ejpam-393	371	7	and	and	CCONJ
ejpam-393	371	8	πb(ιa(y	πb(ιa(y	PROPN
ejpam-393	371	9	)	)	PUNCT
ejpam-393	371	10	)	)	PUNCT
ejpam-393	372	1	=	=	PUNCT
ejpam-393	372	2	0	0	PUNCT
ejpam-393	373	1	if	if	SCONJ
ejpam-393	373	2	a	a	DET
ejpam-393	373	3	6=	6=	PROPN
ejpam-393	373	4	b.	b.	PROPN
ejpam-393	373	5	suppose	suppose	VERB
ejpam-393	373	6	x	x	X
ejpam-393	373	7	∈nrµc	∈nrµc	NOUN
ejpam-393	373	8	\{0	\{0	NOUN
ejpam-393	373	9	}	}	PUNCT
ejpam-393	373	10	.	.	PUNCT
ejpam-393	374	1	since	since	SCONJ
ejpam-393	374	2	x	x	X
ejpam-393	374	3	6=	6=	ADP
ejpam-393	374	4	0	0	NUM
ejpam-393	374	5	,	,	PUNCT
ejpam-393	374	6	it	it	PRON
ejpam-393	374	7	must	must	AUX
ejpam-393	374	8	have	have	VERB
ejpam-393	374	9	a	a	DET
ejpam-393	374	10	non	non	ADJ
ejpam-393	374	11	-	-	ADJ
ejpam-393	374	12	zero	zero	NUM
ejpam-393	374	13	component	component	NOUN
ejpam-393	374	14	πa(x	πa(x	NOUN
ejpam-393	374	15	)	)	PUNCT
ejpam-393	374	16	∈	∈	PROPN
ejpam-393	374	17	da	da	NOUN
ejpam-393	374	18	,	,	PUNCT
ejpam-393	374	19	for	for	SCONJ
ejpam-393	374	20	some	some	PRON
ejpam-393	374	21	a	a	DET
ejpam-393	374	22	∈	∈	PROPN
ejpam-393	374	23	α	α	X
ejpam-393	374	24	.	.	PUNCT
ejpam-393	374	25	say	say	VERB
ejpam-393	374	26	;	;	PUNCT
ejpam-393	374	27	6=	6=	NUM
ejpam-393	374	28	φ(x	φ(x	PROPN
ejpam-393	374	29	i0	i0	PROPN
ejpam-393	374	30	,	,	PUNCT
ejpam-393	374	31	.	.	PUNCT
ejpam-393	374	32	.	.	PUNCT
ejpam-393	375	1	.	.	PUNCT
ejpam-393	376	1	,	,	PUNCT
ejpam-393	376	2	x	x	X
ejpam-393	376	3	ik	ik	X
ejpam-393	376	4	)	)	PUNCT
ejpam-393	376	5	da	da	PROPN
ejpam-393	376	6	=	=	PUNCT
ejpam-393	376	7	πa(x	πa(x	NOUN
ejpam-393	376	8	)	)	PUNCT
ejpam-393	376	9	for	for	ADP
ejpam-393	376	10	some	some	DET
ejpam-393	376	11	l	l	NOUN
ejpam-393	376	12	-	-	NOUN
ejpam-393	376	13	formula	formula	NOUN
ejpam-393	376	14	φ(x	φ(x	PROPN
ejpam-393	376	15	i0	i0	PROPN
ejpam-393	376	16	,	,	PUNCT
ejpam-393	376	17	.	.	PUNCT
ejpam-393	376	18	.	.	PUNCT
ejpam-393	376	19	.	.	PUNCT
ejpam-393	377	1	,	,	PUNCT
ejpam-393	377	2	x	x	X
ejpam-393	377	3	ik	ik	PROPN
ejpam-393	377	4	)	)	PUNCT
ejpam-393	377	5	.	.	PUNCT
ejpam-393	378	1	we	we	PRON
ejpam-393	378	2	have	have	VERB
ejpam-393	378	3	φ(x	φ(x	PROPN
ejpam-393	378	4	i0	i0	PROPN
ejpam-393	378	5	,	,	PUNCT
ejpam-393	378	6	.	.	PUNCT
ejpam-393	378	7	.	.	PUNCT
ejpam-393	378	8	.	.	PUNCT
ejpam-393	379	1	,	,	PUNCT
ejpam-393	379	2	x	x	PROPN
ejpam-393	379	3	ik	ik	X
ejpam-393	379	4	)	)	PUNCT
ejpam-393	379	5	da	da	PROPN
ejpam-393	379	6	∈nrµda	∈nrµda	NUM
ejpam-393	379	7	)	)	PUNCT
ejpam-393	379	8	.	.	PUNCT
ejpam-393	380	1	pick	pick	VERB
ejpam-393	380	2	f	f	PROPN
ejpam-393	380	3	∈	∈	PROPN
ejpam-393	380	4	φ(x	φ(x	PROPN
ejpam-393	380	5	i0	i0	PROPN
ejpam-393	380	6	,	,	PUNCT
ejpam-393	380	7	.	.	PUNCT
ejpam-393	380	8	.	.	PUNCT
ejpam-393	381	1	.	.	PUNCT
ejpam-393	382	1	,	,	PUNCT
ejpam-393	382	2	x	x	X
ejpam-393	382	3	ik	ik	X
ejpam-393	382	4	)	)	PUNCT
ejpam-393	382	5	da	da	PROPN
ejpam-393	383	1	and	and	CCONJ
ejpam-393	383	2	let	let	VERB
ejpam-393	383	3	b	b	X
ejpam-393	383	4	=	=	SYM
ejpam-393	383	5	na	na	PROPN
ejpam-393	383	6	(	(	PUNCT
ejpam-393	383	7	f	f	PROPN
ejpam-393	383	8	(	(	PUNCT
ejpam-393	383	9	0	0	NUM
ejpam-393	383	10	)	)	PUNCT
ejpam-393	383	11	,	,	PUNCT
ejpam-393	383	12	f	f	PROPN
ejpam-393	383	13	(	(	PUNCT
ejpam-393	383	14	1	1	NUM
ejpam-393	383	15	)	)	PUNCT
ejpam-393	383	16	,	,	PUNCT
ejpam-393	383	17	.	.	PUNCT
ejpam-393	383	18	.	.	PUNCT
ejpam-393	384	1	.	.	PUNCT
ejpam-393	385	1	fn−1	fn−1	ADJ
ejpam-393	385	2	)	)	PUNCT
ejpam-393	385	3	∈	∈	PROPN
ejpam-393	385	4	α	α	NOUN
ejpam-393	385	5	.	.	PUNCT
ejpam-393	386	1	we	we	PRON
ejpam-393	386	2	will	will	AUX
ejpam-393	386	3	show	show	VERB
ejpam-393	386	4	that	that	DET
ejpam-393	386	5	b(x0	b(x0	NOUN
ejpam-393	386	6	,	,	PUNCT
ejpam-393	386	7	x1	x1	PROPN
ejpam-393	386	8	,	,	PUNCT
ejpam-393	386	9	.	.	PUNCT
ejpam-393	386	10	.	.	PUNCT
ejpam-393	386	11	.	.	PUNCT
ejpam-393	387	1	xn−1	xn−1	PROPN
ejpam-393	387	2	)	)	PUNCT
ejpam-393	387	3	da	da	PROPN
ejpam-393	387	4	⊆	⊆	NUM
ejpam-393	387	5	φ(x	φ(x	PROPN
ejpam-393	387	6	i0	i0	PROPN
ejpam-393	387	7	,	,	PUNCT
ejpam-393	387	8	.	.	PUNCT
ejpam-393	387	9	.	.	PUNCT
ejpam-393	388	1	.	.	PUNCT
ejpam-393	389	1	,	,	PUNCT
ejpam-393	389	2	x	x	X
ejpam-393	389	3	ik	ik	X
ejpam-393	389	4	)	)	PUNCT
ejpam-393	389	5	da	da	PROPN
ejpam-393	389	6	.	.	PUNCT
ejpam-393	390	1	take	take	VERB
ejpam-393	390	2	any	any	DET
ejpam-393	390	3	g	g	PROPN
ejpam-393	390	4	∈	∈	PROPN
ejpam-393	390	5	b(x0	b(x0	NOUN
ejpam-393	390	6	,	,	PUNCT
ejpam-393	390	7	x1	x1	PROPN
ejpam-393	390	8	.	.	PUNCT
ejpam-393	390	9	.	.	PUNCT
ejpam-393	390	10	.	.	PUNCT
ejpam-393	391	1	xn−1	xn−1	PROPN
ejpam-393	391	2	)	)	PUNCT
ejpam-393	392	1	da	da	NOUN
ejpam-393	392	2	,	,	PUNCT
ejpam-393	392	3	so	so	ADV
ejpam-393	392	4	na(g(0	na(g(0	NOUN
ejpam-393	392	5	)	)	PUNCT
ejpam-393	392	6	,	,	PUNCT
ejpam-393	392	7	g(1	g(1	NOUN
ejpam-393	392	8	)	)	PUNCT
ejpam-393	392	9	.	.	PUNCT
ejpam-393	392	10	.	.	PUNCT
ejpam-393	392	11	.	.	PUNCT
ejpam-393	393	1	g(n−1	g(n−1	PROPN
ejpam-393	393	2	)	)	PUNCT
ejpam-393	393	3	)	)	PUNCT
ejpam-393	394	1	=	=	SYM
ejpam-393	394	2	b.	b.	PROPN
ejpam-393	395	1	the	the	DET
ejpam-393	395	2	map	map	NOUN
ejpam-393	395	3	{	{	PUNCT
ejpam-393	395	4	(	(	PUNCT
ejpam-393	395	5	f	f	X
ejpam-393	395	6	(	(	PUNCT
ejpam-393	395	7	0	0	NUM
ejpam-393	395	8	)	)	PUNCT
ejpam-393	395	9	,	,	PUNCT
ejpam-393	395	10	g(0	g(0	NOUN
ejpam-393	395	11	)	)	PUNCT
ejpam-393	395	12	)	)	PUNCT
ejpam-393	395	13	,	,	PUNCT
ejpam-393	395	14	(	(	PUNCT
ejpam-393	395	15	f	f	X
ejpam-393	395	16	(	(	PUNCT
ejpam-393	395	17	1	1	NUM
ejpam-393	395	18	)	)	PUNCT
ejpam-393	395	19	,	,	PUNCT
ejpam-393	395	20	g(1	g(1	NOUN
ejpam-393	395	21	)	)	PUNCT
ejpam-393	395	22	)	)	PUNCT
ejpam-393	395	23	.	.	PUNCT
ejpam-393	395	24	.	.	PUNCT
ejpam-393	395	25	.	.	PUNCT
ejpam-393	396	1	(	(	PUNCT
ejpam-393	396	2	f	f	X
ejpam-393	396	3	(	(	PUNCT
ejpam-393	396	4	n−1	n−1	PROPN
ejpam-393	396	5	)	)	PUNCT
ejpam-393	396	6	,	,	PUNCT
ejpam-393	396	7	g(n−1	g(n−1	PROPN
ejpam-393	396	8	)	)	PUNCT
ejpam-393	396	9	)	)	PUNCT
ejpam-393	396	10	}	}	PUNCT
ejpam-393	396	11	is	be	AUX
ejpam-393	396	12	a	a	DET
ejpam-393	396	13	partial	partial	ADJ
ejpam-393	396	14	isomorphism	isomorphism	NOUN
ejpam-393	396	15	of	of	ADP
ejpam-393	396	16	na	na	PART
ejpam-393	396	17	.	.	PUNCT
ejpam-393	397	1	by	by	ADP
ejpam-393	397	2	(	(	PUNCT
ejpam-393	397	3	2	2	X
ejpam-393	397	4	)	)	PUNCT
ejpam-393	397	5	this	this	PRON
ejpam-393	397	6	extends	extend	VERB
ejpam-393	397	7	to	to	ADP
ejpam-393	397	8	a	a	DET
ejpam-393	397	9	finite	finite	ADJ
ejpam-393	397	10	partial	partial	ADJ
ejpam-393	397	11	isomorphism	isomorphism	NOUN
ejpam-393	397	12	θ	θ	PROPN
ejpam-393	397	13	of	of	ADP
ejpam-393	397	14	na	na	INTJ
ejpam-393	397	15	whose	whose	DET
ejpam-393	397	16	domain	domain	NOUN
ejpam-393	397	17	includes	include	VERB
ejpam-393	397	18	f	f	PROPN
ejpam-393	397	19	(	(	PUNCT
ejpam-393	397	20	i0	i0	PROPN
ejpam-393	397	21	)	)	PUNCT
ejpam-393	397	22	,	,	PUNCT
ejpam-393	397	23	.	.	PUNCT
ejpam-393	397	24	.	.	PUNCT
ejpam-393	398	1	.	.	PUNCT
ejpam-393	399	1	,	,	PUNCT
ejpam-393	399	2	f	f	PROPN
ejpam-393	399	3	(	(	PUNCT
ejpam-393	399	4	ik	ik	PROPN
ejpam-393	399	5	)	)	PUNCT
ejpam-393	399	6	.	.	PUNCT
ejpam-393	400	1	let	let	VERB
ejpam-393	400	2	g′	g′	NOUN
ejpam-393	400	3	∈	∈	PROPN
ejpam-393	400	4	ua	ua	PROPN
ejpam-393	400	5	be	be	AUX
ejpam-393	400	6	defined	define	VERB
ejpam-393	400	7	by	by	ADP
ejpam-393	400	8	g′(i	g′(i	NOUN
ejpam-393	400	9	)	)	PUNCT
ejpam-393	400	10	=	=	SYM
ejpam-393	400	11	¨	¨	NOUN
ejpam-393	400	12	θ(i	θ(i	PROPN
ejpam-393	400	13	)	)	PUNCT
ejpam-393	400	14	if	if	SCONJ
ejpam-393	400	15	i	i	PRON
ejpam-393	400	16	∈	∈	PROPN
ejpam-393	400	17	dom(θ	dom(θ	PROPN
ejpam-393	400	18	)	)	PUNCT
ejpam-393	400	19	g(i	g(i	NOUN
ejpam-393	400	20	)	)	PUNCT
ejpam-393	400	21	otherwise	otherwise	ADV
ejpam-393	400	22	by	by	ADP
ejpam-393	400	23	(	(	PUNCT
ejpam-393	400	24	3	3	NUM
ejpam-393	400	25	)	)	PUNCT
ejpam-393	400	26	,	,	PUNCT
ejpam-393	400	27	na	na	NOUN
ejpam-393	400	28	,	,	PUNCT
ejpam-393	400	29	g′	g′	NOUN
ejpam-393	400	30	|=	|=	PUNCT
ejpam-393	400	31	φ(x	φ(x	PROPN
ejpam-393	400	32	i0	i0	PROPN
ejpam-393	400	33	,	,	PUNCT
ejpam-393	400	34	.	.	PUNCT
ejpam-393	400	35	.	.	PUNCT
ejpam-393	401	1	.	.	PUNCT
ejpam-393	402	1	,	,	PUNCT
ejpam-393	402	2	x	x	X
ejpam-393	402	3	ik	ik	PROPN
ejpam-393	402	4	)	)	PUNCT
ejpam-393	402	5	.	.	PUNCT
ejpam-393	403	1	observe	observe	VERB
ejpam-393	403	2	that	that	SCONJ
ejpam-393	403	3	g′(0	g′(0	NOUN
ejpam-393	403	4	)	)	PUNCT
ejpam-393	403	5	=	=	SYM
ejpam-393	403	6	θ(0	θ(0	PROPN
ejpam-393	403	7	)	)	PUNCT
ejpam-393	403	8	=	=	SYM
ejpam-393	403	9	g(0	g(0	PROPN
ejpam-393	403	10	)	)	PUNCT
ejpam-393	403	11	and	and	CCONJ
ejpam-393	403	12	similarly	similarly	ADV
ejpam-393	403	13	g′(n	g′(n	PROPN
ejpam-393	404	1	−	−	NUM
ejpam-393	404	2	1	1	NUM
ejpam-393	404	3	)	)	PUNCT
ejpam-393	404	4	=	=	SYM
ejpam-393	404	5	g(n	g(n	PROPN
ejpam-393	404	6	−	−	PROPN
ejpam-393	404	7	1	1	NUM
ejpam-393	404	8	)	)	PUNCT
ejpam-393	404	9	,	,	PUNCT
ejpam-393	404	10	so	so	CCONJ
ejpam-393	404	11	g	g	PROPN
ejpam-393	404	12	is	be	AUX
ejpam-393	404	13	identical	identical	ADJ
ejpam-393	404	14	to	to	ADP
ejpam-393	404	15	g′	g′	NOUN
ejpam-393	404	16	over	over	ADP
ejpam-393	404	17	µ	µ	NOUN
ejpam-393	404	18	and	and	CCONJ
ejpam-393	404	19	it	it	PRON
ejpam-393	404	20	differs	differ	VERB
ejpam-393	404	21	from	from	ADP
ejpam-393	404	22	g′	g′	NOUN
ejpam-393	404	23	on	on	ADP
ejpam-393	404	24	only	only	ADV
ejpam-393	404	25	a	a	DET
ejpam-393	404	26	finite	finite	ADJ
ejpam-393	404	27	set	set	NOUN
ejpam-393	404	28	of	of	ADP
ejpam-393	404	29	coordinates	coordinate	NOUN
ejpam-393	404	30	.	.	PUNCT
ejpam-393	405	1	since	since	SCONJ
ejpam-393	405	2	φ(x	φ(x	PROPN
ejpam-393	405	3	i0	i0	PROPN
ejpam-393	405	4	,	,	PUNCT
ejpam-393	405	5	.	.	PUNCT
ejpam-393	405	6	.	.	PUNCT
ejpam-393	405	7	.	.	PUNCT
ejpam-393	406	1	,	,	PUNCT
ejpam-393	406	2	x	x	PROPN
ejpam-393	406	3	ik	ik	X
ejpam-393	406	4	)	)	PUNCT
ejpam-393	406	5	da	da	PROPN
ejpam-393	406	6	∈	∈	PROPN
ejpam-393	406	7	nrµ(c	nrµ(c	PROPN
ejpam-393	406	8	)	)	PUNCT
ejpam-393	406	9	we	we	PRON
ejpam-393	406	10	deduce	deduce	VERB
ejpam-393	406	11	na	na	ADP
ejpam-393	406	12	,	,	PUNCT
ejpam-393	406	13	g	g	PROPN
ejpam-393	406	14	|=	|=	PUNCT
ejpam-393	406	15	φ(x	φ(x	PROPN
ejpam-393	406	16	i0	i0	PROPN
ejpam-393	406	17	,	,	PUNCT
ejpam-393	406	18	.	.	PUNCT
ejpam-393	406	19	.	.	PUNCT
ejpam-393	407	1	.	.	PUNCT
ejpam-393	408	1	,	,	PUNCT
ejpam-393	408	2	x	x	X
ejpam-393	408	3	ik	ik	PROPN
ejpam-393	408	4	)	)	PUNCT
ejpam-393	408	5	,	,	PUNCT
ejpam-393	408	6	so	so	ADV
ejpam-393	408	7	g	g	PROPN
ejpam-393	408	8	∈	∈	PROPN
ejpam-393	408	9	φ(x	φ(x	PROPN
ejpam-393	408	10	i0	i0	PROPN
ejpam-393	408	11	,	,	PUNCT
ejpam-393	408	12	.	.	PUNCT
ejpam-393	408	13	.	.	PUNCT
ejpam-393	408	14	.	.	PUNCT
ejpam-393	409	1	,	,	PUNCT
ejpam-393	409	2	x	x	X
ejpam-393	409	3	ik	ik	X
ejpam-393	409	4	)	)	PUNCT
ejpam-393	409	5	da	da	PROPN
ejpam-393	409	6	.	.	PUNCT
ejpam-393	410	1	this	this	PRON
ejpam-393	410	2	proves	prove	VERB
ejpam-393	410	3	that	that	SCONJ
ejpam-393	410	4	b(x0	b(x0	NOUN
ejpam-393	410	5	,	,	PUNCT
ejpam-393	410	6	x1	x1	PROPN
ejpam-393	410	7	.	.	PUNCT
ejpam-393	410	8	.	.	PUNCT
ejpam-393	410	9	.	.	PUNCT
ejpam-393	411	1	xµ−1	xµ−1	PROPN
ejpam-393	411	2	)	)	PUNCT
ejpam-393	411	3	da	da	PROPN
ejpam-393	411	4	⊆	⊆	NUM
ejpam-393	411	5	φ(x	φ(x	PROPN
ejpam-393	411	6	i0	i0	PROPN
ejpam-393	411	7	,	,	PUNCT
ejpam-393	411	8	.	.	PUNCT
ejpam-393	411	9	.	.	PUNCT
ejpam-393	412	1	.	.	PUNCT
ejpam-393	413	1	,	,	PUNCT
ejpam-393	413	2	x	x	X
ejpam-393	413	3	ik	ik	X
ejpam-393	413	4	)	)	PUNCT
ejpam-393	413	5	da	da	PROPN
ejpam-393	413	6	=	=	NOUN
ejpam-393	413	7	πa(x	πa(x	NOUN
ejpam-393	413	8	)	)	PUNCT
ejpam-393	413	9	,	,	PUNCT
ejpam-393	413	10	and	and	CCONJ
ejpam-393	413	11	so	so	ADV
ejpam-393	413	12	ιa(b(x0	ιa(b(x0	PROPN
ejpam-393	413	13	,	,	PUNCT
ejpam-393	413	14	x1	x1	PROPN
ejpam-393	413	15	,	,	PUNCT
ejpam-393	413	16	.	.	PUNCT
ejpam-393	413	17	.	.	PUNCT
ejpam-393	413	18	.	.	PUNCT
ejpam-393	414	1	xn−1	xn−1	PROPN
ejpam-393	414	2	)	)	PUNCT
ejpam-393	414	3	da)≤	da)≤	X
ejpam-393	414	4	ιa(φ(x	ιa(φ(x	X
ejpam-393	414	5	i0	i0	PROPN
ejpam-393	414	6	,	,	PUNCT
ejpam-393	414	7	.	.	PUNCT
ejpam-393	414	8	.	.	PUNCT
ejpam-393	414	9	.	.	PUNCT
ejpam-393	415	1	,	,	PUNCT
ejpam-393	415	2	x	x	X
ejpam-393	415	3	ik	ik	X
ejpam-393	415	4	)	)	PUNCT
ejpam-393	415	5	da)≤	da)≤	X
ejpam-393	415	6	x	x	PUNCT
ejpam-393	415	7	∈	∈	PROPN
ejpam-393	415	8	c	c	NOUN
ejpam-393	415	9	\	\	X
ejpam-393	415	10	{	{	PUNCT
ejpam-393	415	11	0	0	NUM
ejpam-393	415	12	}	}	PUNCT
ejpam-393	415	13	.	.	PUNCT
ejpam-393	416	1	hence	hence	ADV
ejpam-393	416	2	every	every	DET
ejpam-393	416	3	non	non	ADJ
ejpam-393	416	4	-	-	ADJ
ejpam-393	416	5	zero	zero	NUM
ejpam-393	416	6	element	element	NOUN
ejpam-393	416	7	x	x	PUNCT
ejpam-393	416	8	of	of	ADP
ejpam-393	416	9	nrnc	nrnc	NOUN
ejpam-393	416	10	is	be	AUX
ejpam-393	416	11	above	above	ADP
ejpam-393	416	12	a	a	DET
ejpam-393	416	13	non	non	ADJ
ejpam-393	416	14	-	-	ADJ
ejpam-393	416	15	zero	zero	NUM
ejpam-393	416	16	element	element	NOUN
ejpam-393	416	17	ιa(b(x0	ιa(b(x0	PROPN
ejpam-393	416	18	,	,	PUNCT
ejpam-393	416	19	x1	x1	PROPN
ejpam-393	416	20	.	.	PUNCT
ejpam-393	416	21	.	.	PUNCT
ejpam-393	416	22	.	.	PUNCT
ejpam-393	417	1	n1	n1	NOUN
ejpam-393	417	2	)	)	PUNCT
ejpam-393	417	3	da	da	NOUN
ejpam-393	417	4	)	)	PUNCT
ejpam-393	417	5	(	(	PUNCT
ejpam-393	417	6	some	some	PRON
ejpam-393	417	7	a	a	PRON
ejpam-393	417	8	,	,	PUNCT
ejpam-393	417	9	b	b	PROPN
ejpam-393	417	10	∈	∈	PROPN
ejpam-393	417	11	α	α	NOUN
ejpam-393	417	12	)	)	PUNCT
ejpam-393	417	13	and	and	CCONJ
ejpam-393	417	14	these	these	DET
ejpam-393	417	15	latter	latter	ADJ
ejpam-393	417	16	elements	element	NOUN
ejpam-393	417	17	are	be	AUX
ejpam-393	417	18	the	the	DET
ejpam-393	417	19	atoms	atom	NOUN
ejpam-393	417	20	of	of	ADP
ejpam-393	417	21	nrnc	nrnc	NOUN
ejpam-393	417	22	.	.	PUNCT
ejpam-393	418	1	so	so	ADV
ejpam-393	418	2	nrnc	nrnc	PROPN
ejpam-393	418	3	is	be	AUX
ejpam-393	418	4	atomic	atomic	ADJ
ejpam-393	418	5	and	and	CCONJ
ejpam-393	418	6	α∼=	α∼=	NUM
ejpam-393	418	7	atnrnc	atnrnc	NOUN
ejpam-393	418	8	—	—	PUNCT
ejpam-393	418	9	the	the	DET
ejpam-393	418	10	isomorphism	isomorphism	NOUN
ejpam-393	418	11	is	be	AUX
ejpam-393	418	12	b	b	PROPN
ejpam-393	418	13	7→	7→	NUM
ejpam-393	418	14	(	(	PUNCT
ejpam-393	418	15	b(x0	b(x0	NOUN
ejpam-393	418	16	,	,	PUNCT
ejpam-393	418	17	x1	x1	PROPN
ejpam-393	418	18	,	,	PUNCT
ejpam-393	418	19	.	.	PUNCT
ejpam-393	418	20	.	.	PUNCT
ejpam-393	418	21	.	.	PUNCT
ejpam-393	419	1	xn−1	xn−1	PROPN
ejpam-393	419	2	)	)	PUNCT
ejpam-393	420	1	da	da	NOUN
ejpam-393	420	2	:	:	PUNCT
ejpam-393	420	3	a	a	DET
ejpam-393	420	4	∈	∈	PROPN
ejpam-393	420	5	a	a	PRON
ejpam-393	420	6	)	)	PUNCT
ejpam-393	420	7	.	.	PUNCT
ejpam-393	421	1	in	in	ADP
ejpam-393	421	2	[	[	X
ejpam-393	421	3	36	36	NUM
ejpam-393	421	4	]	]	PUNCT
ejpam-393	421	5	,	,	PUNCT
ejpam-393	421	6	we	we	PRON
ejpam-393	421	7	use	use	VERB
ejpam-393	421	8	such	such	ADJ
ejpam-393	421	9	games	game	NOUN
ejpam-393	421	10	to	to	PART
ejpam-393	421	11	show	show	VERB
ejpam-393	421	12	that	that	SCONJ
ejpam-393	421	13	for	for	ADP
ejpam-393	421	14	n	n	PRON
ejpam-393	421	15	≥	≥	NOUN
ejpam-393	421	16	3	3	NUM
ejpam-393	421	17	,	,	PUNCT
ejpam-393	421	18	there	there	PRON
ejpam-393	421	19	is	be	VERB
ejpam-393	421	20	a	a	DET
ejpam-393	421	21	representable	representable	ADJ
ejpam-393	421	22	a	a	DET
ejpam-393	421	23	∈	∈	NOUN
ejpam-393	421	24	can	can	AUX
ejpam-393	421	25	with	with	ADP
ejpam-393	421	26	atom	atom	NOUN
ejpam-393	421	27	structure	structure	NOUN
ejpam-393	421	28	α	α	PRON
ejpam-393	421	29	such	such	ADJ
ejpam-393	421	30	that	that	SCONJ
ejpam-393	421	31	∀	∀	NOUN
ejpam-393	421	32	can	can	AUX
ejpam-393	421	33	win	win	VERB
ejpam-393	421	34	the	the	DET
ejpam-393	421	35	game	game	NOUN
ejpam-393	421	36	f	f	PROPN
ejpam-393	421	37	n+2(α	n+2(α	PROPN
ejpam-393	421	38	)	)	PUNCT
ejpam-393	421	39	.	.	PUNCT
ejpam-393	422	1	however	however	ADV
ejpam-393	422	2	∃	∃	PROPN
ejpam-393	422	3	has	have	VERB
ejpam-393	422	4	a	a	DET
ejpam-393	422	5	winning	win	VERB
ejpam-393	422	6	strategy	strategy	NOUN
ejpam-393	422	7	in	in	ADP
ejpam-393	422	8	hn(α	hn(α	NOUN
ejpam-393	422	9	)	)	PUNCT
ejpam-393	422	10	,	,	PUNCT
ejpam-393	422	11	for	for	ADP
ejpam-393	422	12	any	any	DET
ejpam-393	422	13	n	n	NOUN
ejpam-393	422	14	<	<	X
ejpam-393	422	15	ω	ω	NOUN
ejpam-393	422	16	.	.	PUNCT
ejpam-393	423	1	it	it	PRON
ejpam-393	423	2	will	will	AUX
ejpam-393	423	3	follow	follow	VERB
ejpam-393	423	4	that	that	SCONJ
ejpam-393	423	5	there	there	PRON
ejpam-393	423	6	a	a	DET
ejpam-393	423	7	countable	countable	ADJ
ejpam-393	423	8	cylindric	cylindric	ADJ
ejpam-393	423	9	algebra	algebra	NOUN
ejpam-393	423	10	a	a	DET
ejpam-393	423	11	′	′	NUM
ejpam-393	423	12	such	such	ADJ
ejpam-393	423	13	that	that	SCONJ
ejpam-393	423	14	a	a	DET
ejpam-393	423	15	′	′	NUM
ejpam-393	423	16	≡	≡	PROPN
ejpam-393	423	17	a	a	PRON
ejpam-393	423	18	and	and	CCONJ
ejpam-393	423	19	∃	∃	PROPN
ejpam-393	423	20	has	have	VERB
ejpam-393	423	21	a	a	DET
ejpam-393	423	22	winning	win	VERB
ejpam-393	423	23	strategy	strategy	NOUN
ejpam-393	423	24	in	in	ADP
ejpam-393	423	25	h(a	h(a	PROPN
ejpam-393	423	26	′	′	NUM
ejpam-393	423	27	)	)	PUNCT
ejpam-393	423	28	.	.	PUNCT
ejpam-393	424	1	so	so	ADV
ejpam-393	424	2	let	let	VERB
ejpam-393	424	3	k	k	PRON
ejpam-393	424	4	be	be	AUX
ejpam-393	424	5	any	any	DET
ejpam-393	424	6	class	class	NOUN
ejpam-393	424	7	such	such	ADJ
ejpam-393	424	8	that	that	SCONJ
ejpam-393	424	9	nrncaω	nrncaω	PROPN
ejpam-393	424	10	⊆	⊆	NUM
ejpam-393	424	11	k	k	PROPN
ejpam-393	424	12	⊆	⊆	NUM
ejpam-393	424	13	scnrncan+2	scnrncan+2	NOUN
ejpam-393	424	14	.	.	PUNCT
ejpam-393	425	1	a	a	DET
ejpam-393	425	2	′	′	NOUN
ejpam-393	425	3	must	must	AUX
ejpam-393	425	4	belong	belong	VERB
ejpam-393	425	5	to	to	ADP
ejpam-393	425	6	nrn(rcaω	nrn(rcaω	PROPN
ejpam-393	425	7	)	)	PUNCT
ejpam-393	425	8	,	,	PUNCT
ejpam-393	425	9	hencea	hencea	NOUN
ejpam-393	425	10	′	′	NOUN
ejpam-393	426	1	∈	∈	PROPN
ejpam-393	427	1	k	k	X
ejpam-393	427	2	.	.	PUNCT
ejpam-393	428	1	buta	buta	PROPN
ejpam-393	428	2	6∈	6∈	PROPN
ejpam-393	428	3	k	k	PROPN
ejpam-393	428	4	and	and	CCONJ
ejpam-393	428	5	a	a	DET
ejpam-393	428	6	�	�	PROPN
ejpam-393	428	7	a	a	DET
ejpam-393	428	8	′.	′.	NOUN
ejpam-393	428	9	thus	thus	ADV
ejpam-393	428	10	k	k	PROPN
ejpam-393	428	11	is	be	AUX
ejpam-393	428	12	not	not	PART
ejpam-393	428	13	elementary	elementary	ADJ
ejpam-393	428	14	.	.	PUNCT
ejpam-393	429	1	from	from	ADP
ejpam-393	429	2	this	this	PRON
ejpam-393	429	3	it	it	PRON
ejpam-393	429	4	easily	easily	ADV
ejpam-393	429	5	follows	follow	VERB
ejpam-393	429	6	that	that	SCONJ
ejpam-393	429	7	the	the	DET
ejpam-393	429	8	class	class	NOUN
ejpam-393	429	9	of	of	ADP
ejpam-393	429	10	completely	completely	ADV
ejpam-393	429	11	representable	representable	ADJ
ejpam-393	429	12	cylindric	cylindric	ADJ
ejpam-393	429	13	algebras	algebra	NOUN
ejpam-393	429	14	is	be	AUX
ejpam-393	429	15	not	not	PART
ejpam-393	429	16	elementary	elementary	ADJ
ejpam-393	429	17	,	,	PUNCT
ejpam-393	429	18	and	and	CCONJ
ejpam-393	429	19	that	that	SCONJ
ejpam-393	429	20	the	the	DET
ejpam-393	429	21	class	class	NOUN
ejpam-393	429	22	nrncan+k	nrncan+k	ADV
ejpam-393	429	23	for	for	ADP
ejpam-393	429	24	any	any	PRON
ejpam-393	429	25	k	k	PROPN
ejpam-393	429	26	≥	≥	X
ejpam-393	429	27	0	0	NUM
ejpam-393	429	28	is	be	AUX
ejpam-393	429	29	not	not	PART
ejpam-393	429	30	elementary	elementary	ADJ
ejpam-393	429	31	either	either	ADV
ejpam-393	429	32	.	.	PUNCT
ejpam-393	430	1	furthermore	furthermore	ADV
ejpam-393	430	2	the	the	DET
ejpam-393	430	3	constructions	construction	NOUN
ejpam-393	430	4	works	work	VERB
ejpam-393	430	5	for	for	ADP
ejpam-393	430	6	many	many	ADJ
ejpam-393	430	7	variants	variant	NOUN
ejpam-393	430	8	of	of	ADP
ejpam-393	430	9	cylindric	cylindric	ADJ
ejpam-393	430	10	algebras	algebra	NOUN
ejpam-393	430	11	like	like	ADP
ejpam-393	430	12	halmos	halmos	NOUN
ejpam-393	430	13	’	'	PUNCT
ejpam-393	430	14	polyadic	polyadic	ADJ
ejpam-393	430	15	equality	equality	NOUN
ejpam-393	430	16	algebras	algebra	NOUN
ejpam-393	430	17	and	and	CCONJ
ejpam-393	430	18	pinter	pinter	NOUN
ejpam-393	430	19	’s	’s	PART
ejpam-393	430	20	substitution	substitution	NOUN
ejpam-393	430	21	algebras	algebra	NOUN
ejpam-393	430	22	.	.	PUNCT
ejpam-393	431	1	theorem	theorem	NOUN
ejpam-393	431	2	4	4	NUM
ejpam-393	431	3	.	.	PUNCT
ejpam-393	432	1	let	let	VERB
ejpam-393	432	2	3≤	3≤	NUM
ejpam-393	432	3	n	n	CCONJ
ejpam-393	432	4	<	<	X
ejpam-393	432	5	ω	ω	NUM
ejpam-393	432	6	.	.	PUNCT
ejpam-393	433	1	then	then	ADV
ejpam-393	433	2	the	the	DET
ejpam-393	433	3	following	follow	VERB
ejpam-393	433	4	hold	hold	NOUN
ejpam-393	433	5	:	:	PUNCT
ejpam-393	433	6	(	(	PUNCT
ejpam-393	433	7	i	i	NOUN
ejpam-393	433	8	)	)	PUNCT
ejpam-393	433	9	any	any	PRON
ejpam-393	434	1	k	k	NOUN
ejpam-393	434	2	such	such	ADJ
ejpam-393	434	3	that	that	SCONJ
ejpam-393	434	4	nrncaω	nrncaω	PROPN
ejpam-393	434	5	⊆	⊆	NUM
ejpam-393	434	6	k	k	NOUN
ejpam-393	434	7	⊆	⊆	NUM
ejpam-393	434	8	scnrncan+2	scnrncan+2	PROPN
ejpam-393	434	9	is	be	AUX
ejpam-393	434	10	not	not	PART
ejpam-393	434	11	elementary	elementary	ADJ
ejpam-393	434	12	.	.	PUNCT
ejpam-393	435	1	(	(	PUNCT
ejpam-393	435	2	ii	ii	X
ejpam-393	435	3	)	)	PUNCT
ejpam-393	435	4	the	the	DET
ejpam-393	435	5	inclusions	inclusion	NOUN
ejpam-393	435	6	nrncaω	nrncaω	ADV
ejpam-393	435	7	⊆	⊆	NUM
ejpam-393	435	8	scnrncaω	scnrncaω	PROPN
ejpam-393	435	9	⊆	⊆	NUM
ejpam-393	435	10	snrncaω	snrncaω	NOUN
ejpam-393	435	11	are	be	AUX
ejpam-393	435	12	all	all	PRON
ejpam-393	435	13	proper	proper	ADJ
ejpam-393	435	14	proof	proof	NOUN
ejpam-393	435	15	.	.	PUNCT
ejpam-393	436	1	(	(	PUNCT
ejpam-393	436	2	i	i	NOUN
ejpam-393	436	3	)	)	PUNCT
ejpam-393	436	4	is	be	AUX
ejpam-393	436	5	already	already	ADV
ejpam-393	436	6	mentioned	mention	VERB
ejpam-393	436	7	.	.	PUNCT
ejpam-393	437	1	while	while	SCONJ
ejpam-393	437	2	for	for	ADP
ejpam-393	437	3	(	(	PUNCT
ejpam-393	437	4	ii	ii	NOUN
ejpam-393	437	5	)	)	PUNCT
ejpam-393	437	6	,	,	PUNCT
ejpam-393	437	7	for	for	ADP
ejpam-393	437	8	the	the	DET
ejpam-393	437	9	first	first	ADJ
ejpam-393	437	10	inclusion	inclusion	NOUN
ejpam-393	437	11	[	[	X
ejpam-393	437	12	18	18	NUM
ejpam-393	437	13	]	]	PUNCT
ejpam-393	437	14	,	,	PUNCT
ejpam-393	437	15	and	and	CCONJ
ejpam-393	437	16	for	for	ADP
ejpam-393	437	17	the	the	DET
ejpam-393	437	18	second	second	ADJ
ejpam-393	437	19	[	[	X
ejpam-393	437	20	8	8	NUM
ejpam-393	437	21	]	]	PUNCT
ejpam-393	437	22	.	.	PUNCT
ejpam-393	438	1	t.	t.	PROPN
ejpam-393	438	2	ahmed	ahmed	PROPN
ejpam-393	438	3	/	/	SYM
ejpam-393	438	4	eur	eur	PROPN
ejpam-393	438	5	.	.	PUNCT
ejpam-393	439	1	j.	j.	PROPN
ejpam-393	439	2	pure	pure	PROPN
ejpam-393	439	3	appl	appl	PROPN
ejpam-393	439	4	.	.	PROPN
ejpam-393	439	5	math	math	PROPN
ejpam-393	439	6	,	,	PUNCT
ejpam-393	439	7	3	3	NUM
ejpam-393	439	8	(	(	PUNCT
ejpam-393	439	9	2010	2010	NUM
ejpam-393	439	10	)	)	PUNCT
ejpam-393	439	11	,	,	PUNCT
ejpam-393	439	12	853	853	NUM
ejpam-393	439	13	-	-	SYM
ejpam-393	439	14	880	880	NUM
ejpam-393	439	15	862	862	NUM
ejpam-393	439	16	2	2	NUM
ejpam-393	439	17	.	.	PUNCT
ejpam-393	440	1	other	other	ADJ
ejpam-393	440	2	algebras	algebra	NOUN
ejpam-393	440	3	now	now	ADV
ejpam-393	440	4	we	we	PRON
ejpam-393	440	5	turn	turn	VERB
ejpam-393	440	6	our	our	PRON
ejpam-393	440	7	attention	attention	NOUN
ejpam-393	440	8	for	for	ADP
ejpam-393	440	9	other	other	ADJ
ejpam-393	440	10	algebras	algebra	NOUN
ejpam-393	440	11	for	for	ADP
ejpam-393	440	12	which	which	PRON
ejpam-393	440	13	the	the	DET
ejpam-393	440	14	notion	notion	NOUN
ejpam-393	440	15	of	of	ADP
ejpam-393	440	16	neat	neat	ADJ
ejpam-393	440	17	reducts	reduct	NOUN
ejpam-393	440	18	make	make	VERB
ejpam-393	440	19	sense	sense	NOUN
ejpam-393	440	20	.	.	PUNCT
ejpam-393	441	1	scn	scn	PROPN
ejpam-393	441	2	,	,	PUNCT
ejpam-393	441	3	can	can	AUX
ejpam-393	441	4	,	,	PUNCT
ejpam-393	441	5	qan	qan	PROPN
ejpam-393	441	6	and	and	CCONJ
ejpam-393	441	7	qean	qean	ADJ
ejpam-393	441	8	abbreviate	abbreviate	VERB
ejpam-393	441	9	the	the	DET
ejpam-393	441	10	classes	class	NOUN
ejpam-393	441	11	of	of	ADP
ejpam-393	441	12	substitution	substitution	NOUN
ejpam-393	441	13	,	,	PUNCT
ejpam-393	441	14	cylindric	cylindric	ADJ
ejpam-393	441	15	,	,	PUNCT
ejpam-393	441	16	quasipolyadic	quasipolyadic	ADJ
ejpam-393	441	17	,	,	PUNCT
ejpam-393	441	18	and	and	CCONJ
ejpam-393	441	19	quasipolyadic	quasipolyadic	ADJ
ejpam-393	441	20	equality	equality	NOUN
ejpam-393	441	21	algebras	algebra	NOUN
ejpam-393	441	22	,	,	PUNCT
ejpam-393	441	23	of	of	ADP
ejpam-393	441	24	dimension	dimension	NOUN
ejpam-393	441	25	n	n	CCONJ
ejpam-393	441	26	,	,	PUNCT
ejpam-393	441	27	respectively	respectively	ADV
ejpam-393	441	28	.	.	PUNCT
ejpam-393	442	1	such	such	ADJ
ejpam-393	442	2	algebras	algebra	NOUN
ejpam-393	442	3	are	be	AUX
ejpam-393	442	4	studied	study	VERB
ejpam-393	442	5	in	in	ADP
ejpam-393	442	6	e.g.	e.g.	ADV
ejpam-393	442	7	[	[	X
ejpam-393	442	8	45	45	NUM
ejpam-393	442	9	,	,	PUNCT
ejpam-393	442	10	34	34	NUM
ejpam-393	442	11	,	,	PUNCT
ejpam-393	442	12	21	21	NUM
ejpam-393	442	13	,	,	PUNCT
ejpam-393	442	14	22	22	NUM
ejpam-393	442	15	,	,	PUNCT
ejpam-393	442	16	24	24	NUM
ejpam-393	442	17	,	,	PUNCT
ejpam-393	442	18	2	2	NUM
ejpam-393	442	19	,	,	PUNCT
ejpam-393	442	20	15	15	NUM
ejpam-393	442	21	,	,	PUNCT
ejpam-393	442	22	29	29	NUM
ejpam-393	442	23	,	,	PUNCT
ejpam-393	442	24	33	33	NUM
ejpam-393	442	25	]	]	PUNCT
ejpam-393	442	26	.	.	PUNCT
ejpam-393	443	1	dfn	dfn	NOUN
ejpam-393	443	2	stands	stand	VERB
ejpam-393	443	3	for	for	ADP
ejpam-393	443	4	the	the	DET
ejpam-393	443	5	class	class	NOUN
ejpam-393	443	6	of	of	ADP
ejpam-393	443	7	diagonal	diagonal	ADJ
ejpam-393	443	8	free	free	ADJ
ejpam-393	443	9	cylindric	cylindric	ADJ
ejpam-393	443	10	algebras	algebra	NOUN
ejpam-393	443	11	.	.	PUNCT
ejpam-393	444	1	it	it	PRON
ejpam-393	444	2	is	be	AUX
ejpam-393	444	3	known	know	VERB
ejpam-393	444	4	,	,	PUNCT
ejpam-393	444	5	and	and	CCONJ
ejpam-393	444	6	indeed	indeed	ADV
ejpam-393	444	7	easy	easy	ADJ
ejpam-393	444	8	to	to	PART
ejpam-393	444	9	show	show	VERB
ejpam-393	444	10	,	,	PUNCT
ejpam-393	444	11	that	that	SCONJ
ejpam-393	444	12	for	for	ADP
ejpam-393	444	13	1	1	NUM
ejpam-393	444	14	<	<	X
ejpam-393	444	15	n	n	X
ejpam-393	444	16	<	<	X
ejpam-393	444	17	m	m	PROPN
ejpam-393	444	18	,	,	PUNCT
ejpam-393	444	19	the	the	DET
ejpam-393	444	20	class	class	NOUN
ejpam-393	444	21	nrndfm	nrndfm	NOUN
ejpam-393	444	22	of	of	ADP
ejpam-393	444	23	neat	neat	ADJ
ejpam-393	444	24	n	n	NOUN
ejpam-393	444	25	-	-	PUNCT
ejpam-393	444	26	reducts	reduct	NOUN
ejpam-393	444	27	of	of	ADP
ejpam-393	444	28	dfm	dfm	PROPN
ejpam-393	444	29	is	be	AUX
ejpam-393	444	30	a	a	DET
ejpam-393	444	31	variety	variety	NOUN
ejpam-393	444	32	.	.	PUNCT
ejpam-393	445	1	in	in	ADP
ejpam-393	445	2	fact	fact	NOUN
ejpam-393	445	3	,	,	PUNCT
ejpam-393	445	4	it	it	PRON
ejpam-393	445	5	is	be	AUX
ejpam-393	445	6	equal	equal	ADJ
ejpam-393	445	7	to	to	ADP
ejpam-393	445	8	dfn	dfn	PROPN
ejpam-393	445	9	[	[	X
ejpam-393	445	10	12][5.1.2	12][5.1.2	X
ejpam-393	445	11	]	]	X
ejpam-393	445	12	.	.	PUNCT
ejpam-393	446	1	in	in	ADP
ejpam-393	446	2	particular	particular	ADJ
ejpam-393	446	3	,	,	PUNCT
ejpam-393	446	4	it	it	PRON
ejpam-393	446	5	is	be	AUX
ejpam-393	446	6	an	an	DET
ejpam-393	446	7	elementary	elementary	ADJ
ejpam-393	446	8	class	class	NOUN
ejpam-393	446	9	.	.	PUNCT
ejpam-393	447	1	on	on	ADP
ejpam-393	447	2	the	the	DET
ejpam-393	447	3	other	other	ADJ
ejpam-393	447	4	hand	hand	NOUN
ejpam-393	447	5	,	,	PUNCT
ejpam-393	447	6	it	it	PRON
ejpam-393	447	7	is	be	AUX
ejpam-393	447	8	known	know	VERB
ejpam-393	447	9	[	[	X
ejpam-393	447	10	18	18	NUM
ejpam-393	447	11	]	]	PUNCT
ejpam-393	447	12	that	that	SCONJ
ejpam-393	447	13	for	for	ADP
ejpam-393	447	14	1	1	NUM
ejpam-393	447	15	<	<	X
ejpam-393	447	16	n	n	X
ejpam-393	447	17	<	<	X
ejpam-393	447	18	m	m	VERB
ejpam-393	447	19	the	the	DET
ejpam-393	447	20	class	class	NOUN
ejpam-393	447	21	nrncam	nrncam	NOUN
ejpam-393	447	22	is	be	AUX
ejpam-393	447	23	not	not	PART
ejpam-393	447	24	an	an	DET
ejpam-393	447	25	elementary	elementary	ADJ
ejpam-393	447	26	class	class	NOUN
ejpam-393	447	27	.	.	PUNCT
ejpam-393	448	1	it	it	PRON
ejpam-393	448	2	is	be	AUX
ejpam-393	448	3	also	also	ADV
ejpam-393	448	4	known	know	VERB
ejpam-393	448	5	[	[	PUNCT
ejpam-393	448	6	29	29	NUM
ejpam-393	448	7	]	]	PUNCT
ejpam-393	448	8	,	,	PUNCT
ejpam-393	448	9	[	[	X
ejpam-393	448	10	34	34	NUM
ejpam-393	448	11	]	]	PUNCT
ejpam-393	448	12	that	that	SCONJ
ejpam-393	448	13	nrnqam	nrnqam	PROPN
ejpam-393	448	14	and	and	CCONJ
ejpam-393	448	15	nrnqeam	nrnqeam	NOUN
ejpam-393	448	16	are	be	AUX
ejpam-393	448	17	not	not	PART
ejpam-393	448	18	elementary	elementary	ADJ
ejpam-393	448	19	classes	class	NOUN
ejpam-393	448	20	.	.	PUNCT
ejpam-393	449	1	it	it	PRON
ejpam-393	449	2	is	be	AUX
ejpam-393	449	3	proved	prove	VERB
ejpam-393	449	4	in	in	ADP
ejpam-393	449	5	op.cit	op.cit	NOUN
ejpam-393	449	6	that	that	SCONJ
ejpam-393	449	7	such	such	ADJ
ejpam-393	449	8	classes	class	NOUN
ejpam-393	449	9	are	be	AUX
ejpam-393	449	10	not	not	PART
ejpam-393	449	11	closed	close	VERB
ejpam-393	449	12	under	under	ADP
ejpam-393	449	13	ultraroots	ultraroot	NOUN
ejpam-393	449	14	.	.	PUNCT
ejpam-393	450	1	so	so	ADV
ejpam-393	450	2	what	what	PRON
ejpam-393	450	3	about	about	ADP
ejpam-393	450	4	reducts	reduct	NOUN
ejpam-393	450	5	,	,	PUNCT
ejpam-393	450	6	i.e	i.e	PRON
ejpam-393	450	7	algebras	algebra	NOUN
ejpam-393	450	8	“	"	PUNCT
ejpam-393	450	9	in	in	ADP
ejpam-393	450	10	between	between	ADP
ejpam-393	450	11	”	"	PUNCT
ejpam-393	450	12	df	df	PROPN
ejpam-393	450	13	and	and	CCONJ
ejpam-393	450	14	ca	can	AUX
ejpam-393	450	15	.	.	PUNCT
ejpam-393	451	1	by	by	ADP
ejpam-393	451	2	“	"	PUNCT
ejpam-393	451	3	in	in	ADP
ejpam-393	451	4	between	between	ADP
ejpam-393	451	5	”	"	PUNCT
ejpam-393	451	6	we	we	PRON
ejpam-393	451	7	mean	mean	VERB
ejpam-393	451	8	a	a	DET
ejpam-393	451	9	class	class	NOUN
ejpam-393	451	10	km	km	NOUN
ejpam-393	451	11	that	that	PRON
ejpam-393	451	12	is	be	AUX
ejpam-393	451	13	a	a	DET
ejpam-393	451	14	reduct	reduct	NOUN
ejpam-393	451	15	of	of	ADP
ejpam-393	451	16	cam	cam	NOUN
ejpam-393	451	17	and	and	CCONJ
ejpam-393	451	18	an	an	DET
ejpam-393	451	19	expansion	expansion	NOUN
ejpam-393	451	20	of	of	ADP
ejpam-393	451	21	dfm	dfm	PROPN
ejpam-393	451	22	.	.	PUNCT
ejpam-393	452	1	a	a	DET
ejpam-393	452	2	typical	typical	ADJ
ejpam-393	452	3	example	example	NOUN
ejpam-393	452	4	is	be	AUX
ejpam-393	452	5	the	the	DET
ejpam-393	452	6	class	class	NOUN
ejpam-393	452	7	scm	scm	PROPN
ejpam-393	453	1	[	[	X
ejpam-393	453	2	15	15	NUM
ejpam-393	453	3	]	]	PUNCT
ejpam-393	453	4	.	.	PUNCT
ejpam-393	454	1	we	we	PRON
ejpam-393	454	2	define	define	VERB
ejpam-393	454	3	another	another	DET
ejpam-393	454	4	reduct	reduct	NOUN
ejpam-393	454	5	rscm	rscm	NOUN
ejpam-393	454	6	(	(	PUNCT
ejpam-393	454	7	class	class	NOUN
ejpam-393	454	8	of	of	ADP
ejpam-393	454	9	algebras	algebra	NOUN
ejpam-393	454	10	of	of	ADP
ejpam-393	454	11	dimension	dimension	NOUN
ejpam-393	454	12	m	m	PROPN
ejpam-393	454	13	)	)	PUNCT
ejpam-393	454	14	which	which	PRON
ejpam-393	454	15	is	be	AUX
ejpam-393	454	16	a	a	DET
ejpam-393	454	17	(	(	PUNCT
ejpam-393	454	18	proper	proper	ADJ
ejpam-393	454	19	)	)	PUNCT
ejpam-393	454	20	reduct	reduct	PROPN
ejpam-393	454	21	of	of	ADP
ejpam-393	454	22	scm	scm	PROPN
ejpam-393	454	23	,	,	PUNCT
ejpam-393	454	24	which	which	PRON
ejpam-393	454	25	in	in	ADP
ejpam-393	454	26	turn	turn	NOUN
ejpam-393	454	27	is	be	AUX
ejpam-393	454	28	a	a	DET
ejpam-393	454	29	reduct	reduct	NOUN
ejpam-393	454	30	of	of	ADP
ejpam-393	454	31	cam	cam	PROPN
ejpam-393	454	32	,	,	PUNCT
ejpam-393	454	33	qam	qam	PROPN
ejpam-393	454	34	qeam	qeam	NOUN
ejpam-393	454	35	.	.	PUNCT
ejpam-393	455	1	definition	definition	NOUN
ejpam-393	455	2	5	5	NUM
ejpam-393	455	3	.	.	PUNCT
ejpam-393	456	1	let	let	VERB
ejpam-393	456	2	m	m	PRON
ejpam-393	456	3	be	be	AUX
ejpam-393	456	4	an	an	DET
ejpam-393	456	5	ordinal	ordinal	ADJ
ejpam-393	456	6	.	.	PUNCT
ejpam-393	457	1	a	a	DET
ejpam-393	457	2	∈	∈	PROPN
ejpam-393	457	3	rscm	rscm	NOUN
ejpam-393	457	4	,	,	PUNCT
ejpam-393	457	5	is	be	AUX
ejpam-393	457	6	defined	define	VERB
ejpam-393	457	7	to	to	PART
ejpam-393	457	8	be	be	AUX
ejpam-393	457	9	an	an	DET
ejpam-393	457	10	algebra	algebra	NOUN
ejpam-393	457	11	a	a	DET
ejpam-393	457	12	=	=	SYM
ejpam-393	457	13	〈	〈	NOUN
ejpam-393	457	14	a,+	a,+	NOUN
ejpam-393	457	15	,	,	PUNCT
ejpam-393	457	16	.,−0,1,ci	.,−0,1,ci	PROPN
ejpam-393	457	17	,	,	PUNCT
ejpam-393	457	18	s	s	VERB
ejpam-393	457	19	j	j	PROPN
ejpam-393	457	20	i	i	PROPN
ejpam-393	457	21	〉	〉	VERB
ejpam-393	457	22	i	i	VERB
ejpam-393	457	23	,	,	PUNCT
ejpam-393	457	24	j∈m	j∈m	VERB
ejpam-393	457	25	obeying	obey	VERB
ejpam-393	457	26	the	the	DET
ejpam-393	457	27	following	following	ADJ
ejpam-393	457	28	axioms	axiom	NOUN
ejpam-393	457	29	for	for	ADP
ejpam-393	457	30	x	x	SYM
ejpam-393	457	31	,	,	PUNCT
ejpam-393	457	32	y	y	PROPN
ejpam-393	457	33	∈	∈	PROPN
ejpam-393	457	34	a	a	PRON
ejpam-393	457	35	and	and	CCONJ
ejpam-393	457	36	i	i	PROPN
ejpam-393	457	37	,	,	PUNCT
ejpam-393	457	38	j	j	PROPN
ejpam-393	457	39	,	,	PUNCT
ejpam-393	457	40	k	k	PROPN
ejpam-393	457	41	,	,	PUNCT
ejpam-393	457	42	l	l	X
ejpam-393	457	43	<	<	X
ejpam-393	457	44	m	m	X
ejpam-393	457	45	:	:	PUNCT
ejpam-393	457	46	(	(	PUNCT
ejpam-393	457	47	e0	e0	PROPN
ejpam-393	457	48	)	)	PUNCT
ejpam-393	458	1	〈	〈	PROPN
ejpam-393	458	2	a,+	a,+	NOUN
ejpam-393	458	3	,	,	PUNCT
ejpam-393	458	4	.,−	.,−	NUM
ejpam-393	458	5	,	,	PUNCT
ejpam-393	458	6	0,1	0,1	NUM
ejpam-393	458	7	〉	〉	NOUN
ejpam-393	458	8	is	be	AUX
ejpam-393	458	9	a	a	DET
ejpam-393	458	10	boolean	boolean	ADJ
ejpam-393	458	11	algebra	algebra	NOUN
ejpam-393	458	12	(	(	PUNCT
ejpam-393	458	13	e1	e1	PROPN
ejpam-393	458	14	)	)	PUNCT
ejpam-393	458	15	c	c	PROPN
ejpam-393	458	16	j0=	j0=	PROPN
ejpam-393	458	17	0	0	NUM
ejpam-393	458	18	,	,	PUNCT
ejpam-393	458	19	x	x	SYM
ejpam-393	458	20	≤	≤	NUM
ejpam-393	458	21	ci	ci	NOUN
ejpam-393	458	22	x	x	NOUN
ejpam-393	458	23	,	,	PUNCT
ejpam-393	458	24	ci(xci	ci(xci	PROPN
ejpam-393	458	25	y	y	PROPN
ejpam-393	458	26	)	)	PUNCT
ejpam-393	459	1	=	=	SYM
ejpam-393	459	2	ci	ci	NOUN
ejpam-393	459	3	x	x	SYM
ejpam-393	459	4	.ci	.ci	PUNCT
ejpam-393	459	5	y	y	NOUN
ejpam-393	459	6	,	,	PUNCT
ejpam-393	459	7	and	and	CCONJ
ejpam-393	459	8	cic	cic	VERB
ejpam-393	459	9	j	j	PROPN
ejpam-393	459	10	x	x	PROPN
ejpam-393	459	11	=	=	SYM
ejpam-393	459	12	c	c	PROPN
ejpam-393	459	13	jci	jci	PROPN
ejpam-393	459	14	x	x	PROPN
ejpam-393	459	15	,	,	PUNCT
ejpam-393	459	16	and	and	CCONJ
ejpam-393	459	17	si	si	INTJ
ejpam-393	459	18	i	i	NOUN
ejpam-393	459	19	x	x	PROPN
ejpam-393	460	1	=	=	PUNCT
ejpam-393	460	2	x	x	PROPN
ejpam-393	460	3	in	in	ADP
ejpam-393	460	4	other	other	ADJ
ejpam-393	460	5	words	word	NOUN
ejpam-393	460	6	the	the	DET
ejpam-393	460	7	cis	cis	NOUN
ejpam-393	460	8	are	be	AUX
ejpam-393	460	9	complemented	complement	VERB
ejpam-393	460	10	closure	closure	NOUN
ejpam-393	460	11	operators	operator	NOUN
ejpam-393	460	12	and	and	CCONJ
ejpam-393	460	13	ci	ci	NOUN
ejpam-393	460	14	,	,	PUNCT
ejpam-393	460	15	c	c	PROPN
ejpam-393	460	16	j	j	PROPN
ejpam-393	460	17	commute	commute	PROPN
ejpam-393	460	18	.	.	PUNCT
ejpam-393	461	1	(	(	PUNCT
ejpam-393	461	2	e2	e2	PROPN
ejpam-393	461	3	)	)	PUNCT
ejpam-393	461	4	s	s	PROPN
ejpam-393	462	1	i	i	PRON
ejpam-393	462	2	i	i	NOUN
ejpam-393	462	3	x	x	PUNCT
ejpam-393	463	1	=	=	PUNCT
ejpam-393	463	2	x	x	X
ejpam-393	463	3	(	(	PUNCT
ejpam-393	463	4	e3	e3	X
ejpam-393	463	5	)	)	PUNCT
ejpam-393	463	6	s	s	VERB
ejpam-393	464	1	i	i	PRON
ejpam-393	464	2	j	j	PROPN
ejpam-393	464	3	are	be	AUX
ejpam-393	464	4	boolean	boolean	ADJ
ejpam-393	464	5	endomorphisms	endomorphism	NOUN
ejpam-393	464	6	.	.	PUNCT
ejpam-393	465	1	(	(	PUNCT
ejpam-393	465	2	e4	e4	PROPN
ejpam-393	465	3	)	)	PUNCT
ejpam-393	465	4	s	s	PART
ejpam-393	466	1	i	i	PRON
ejpam-393	466	2	j	j	PROPN
ejpam-393	466	3	ci	ci	NOUN
ejpam-393	466	4	x	x	PUNCT
ejpam-393	467	1	=	=	PUNCT
ejpam-393	467	2	ci	ci	PROPN
ejpam-393	467	3	x	x	X
ejpam-393	467	4	(	(	PUNCT
ejpam-393	467	5	e5	e5	NOUN
ejpam-393	467	6	)	)	PUNCT
ejpam-393	467	7	cis	cis	NOUN
ejpam-393	468	1	i	i	PRON
ejpam-393	468	2	j	j	PROPN
ejpam-393	469	1	x	x	PUNCT
ejpam-393	469	2	=	=	PUNCT
ejpam-393	469	3	si	si	PROPN
ejpam-393	469	4	j	j	PROPN
ejpam-393	469	5	x	x	INTJ
ejpam-393	469	6	whenever	whenever	SCONJ
ejpam-393	469	7	i	i	PRON
ejpam-393	469	8	6=	6=	PROPN
ejpam-393	469	9	j	j	PROPN
ejpam-393	469	10	(	(	PUNCT
ejpam-393	469	11	e6	e6	PROPN
ejpam-393	469	12	)	)	PUNCT
ejpam-393	469	13	s	s	VERB
ejpam-393	469	14	i	i	PRON
ejpam-393	469	15	j	j	NOUN
ejpam-393	469	16	ck	ck	INTJ
ejpam-393	469	17	x	x	X
ejpam-393	470	1	=	=	PUNCT
ejpam-393	470	2	cks	ck	NOUN
ejpam-393	471	1	i	i	PRON
ejpam-393	471	2	j	j	PROPN
ejpam-393	471	3	x	x	X
ejpam-393	471	4	,	,	PUNCT
ejpam-393	471	5	whenever	whenever	SCONJ
ejpam-393	471	6	k	k	PROPN
ejpam-393	471	7	/∈	/∈	PUNCT
ejpam-393	471	8	{	{	PUNCT
ejpam-393	471	9	i	i	PROPN
ejpam-393	471	10	,	,	PUNCT
ejpam-393	471	11	j	j	PROPN
ejpam-393	471	12	}	}	PUNCT
ejpam-393	471	13	(	(	PUNCT
ejpam-393	471	14	e7	e7	PROPN
ejpam-393	471	15	)	)	PUNCT
ejpam-393	472	1	cis	cis	NOUN
ejpam-393	472	2	j	j	NOUN
ejpam-393	472	3	i	i	NOUN
ejpam-393	472	4	x	x	PUNCT
ejpam-393	472	5	=	=	PUNCT
ejpam-393	473	1	c	c	X
ejpam-393	473	2	js	js	INTJ
ejpam-393	474	1	i	i	PRON
ejpam-393	474	2	j	j	PROPN
ejpam-393	474	3	x	x	X
ejpam-393	474	4	(	(	PUNCT
ejpam-393	474	5	e8	e8	PROPN
ejpam-393	474	6	)	)	PUNCT
ejpam-393	474	7	s	s	PROPN
ejpam-393	475	1	i	i	PRON
ejpam-393	475	2	j	j	INTJ
ejpam-393	475	3	sk	sk	INTJ
ejpam-393	476	1	i	i	PROPN
ejpam-393	476	2	ci	ci	PROPN
ejpam-393	476	3	x	x	PUNCT
ejpam-393	477	1	=	=	PRON
ejpam-393	477	2	sk	sk	PROPN
ejpam-393	477	3	j	j	PROPN
ejpam-393	477	4	ci	ci	PROPN
ejpam-393	477	5	x	x	X
ejpam-393	477	6	(	(	PUNCT
ejpam-393	477	7	e9	e9	PROPN
ejpam-393	477	8	)	)	PUNCT
ejpam-393	477	9	s	s	PART
ejpam-393	477	10	j	j	NOUN
ejpam-393	478	1	i	i	PRON
ejpam-393	478	2	sl	sl	VERB
ejpam-393	478	3	k	k	NOUN
ejpam-393	479	1	x	x	PUNCT
ejpam-393	480	1	=	=	PUNCT
ejpam-393	481	1	sl	sl	NUM
ejpam-393	481	2	k	k	PROPN
ejpam-393	481	3	s	s	PROPN
ejpam-393	481	4	j	j	PROPN
ejpam-393	482	1	i	i	NOUN
ejpam-393	482	2	x	x	VERB
ejpam-393	482	3	when	when	SCONJ
ejpam-393	482	4	|{i	|{i	X
ejpam-393	482	5	,	,	PUNCT
ejpam-393	482	6	j	j	PROPN
ejpam-393	482	7	,	,	PUNCT
ejpam-393	482	8	k	k	PROPN
ejpam-393	482	9	,	,	PUNCT
ejpam-393	482	10	l}|	l}|	PROPN
ejpam-393	482	11	=	=	SYM
ejpam-393	482	12	4	4	NUM
ejpam-393	482	13	definition	definition	NOUN
ejpam-393	482	14	6	6	NUM
ejpam-393	482	15	.	.	PUNCT
ejpam-393	483	1	(	(	PUNCT
ejpam-393	483	2	i	i	NOUN
ejpam-393	483	3	)	)	PUNCT
ejpam-393	483	4	let	let	VERB
ejpam-393	483	5	n	n	PRON
ejpam-393	483	6	<	<	X
ejpam-393	483	7	m	m	AUX
ejpam-393	483	8	be	be	VERB
ejpam-393	483	9	ordinals	ordinal	NOUN
ejpam-393	483	10	.	.	PUNCT
ejpam-393	484	1	let	let	VERB
ejpam-393	484	2	b	b	X
ejpam-393	484	3	∈	∈	PROPN
ejpam-393	484	4	rscm	rscm	NOUN
ejpam-393	484	5	then	then	ADV
ejpam-393	484	6	the	the	DET
ejpam-393	484	7	neat	neat	ADJ
ejpam-393	484	8	n	n	NOUN
ejpam-393	484	9	-	-	PUNCT
ejpam-393	484	10	reduct	reduct	NOUN
ejpam-393	484	11	of	of	ADP
ejpam-393	484	12	b	b	PROPN
ejpam-393	484	13	,	,	PUNCT
ejpam-393	484	14	in	in	ADP
ejpam-393	484	15	symbols	symbol	NOUN
ejpam-393	484	16	nrnb	nrnb	ADV
ejpam-393	484	17	is	be	AUX
ejpam-393	484	18	the	the	DET
ejpam-393	484	19	rscn	rscn	NOUN
ejpam-393	484	20	with	with	ADP
ejpam-393	484	21	universe	universe	NOUN
ejpam-393	484	22	n	n	NOUN
ejpam-393	484	23	rnb	rnb	NOUN
ejpam-393	485	1	=	=	PUNCT
ejpam-393	485	2	{	{	PUNCT
ejpam-393	485	3	b	b	PROPN
ejpam-393	485	4	∈	∈	PROPN
ejpam-393	485	5	b	b	PROPN
ejpam-393	485	6	:	:	PUNCT
ejpam-393	485	7	ci	ci	PROPN
ejpam-393	485	8	b	b	PROPN
ejpam-393	485	9	=	=	SYM
ejpam-393	485	10	b	b	PROPN
ejpam-393	485	11	for	for	ADP
ejpam-393	485	12	all	all	DET
ejpam-393	485	13	n≤	n≤	PRON
ejpam-393	485	14	i	i	PRON
ejpam-393	485	15	<	<	X
ejpam-393	485	16	m	m	VERB
ejpam-393	485	17	}	}	PUNCT
ejpam-393	485	18	,	,	PUNCT
ejpam-393	485	19	and	and	CCONJ
ejpam-393	485	20	whose	whose	DET
ejpam-393	485	21	operations	operation	NOUN
ejpam-393	485	22	are	be	AUX
ejpam-393	485	23	those	those	PRON
ejpam-393	485	24	of	of	ADP
ejpam-393	485	25	the	the	DET
ejpam-393	485	26	similarity	similarity	NOUN
ejpam-393	485	27	type	type	NOUN
ejpam-393	485	28	of	of	ADP
ejpam-393	485	29	scm	scm	PROPN
ejpam-393	485	30	(	(	PUNCT
ejpam-393	485	31	evaluated	evaluate	VERB
ejpam-393	485	32	in	in	ADP
ejpam-393	485	33	b	b	PROPN
ejpam-393	485	34	and	and	CCONJ
ejpam-393	485	35	)	)	PUNCT
ejpam-393	485	36	restricted	restrict	VERB
ejpam-393	485	37	to	to	ADP
ejpam-393	485	38	n	n	PRON
ejpam-393	485	39	rnb	rnb	NOUN
ejpam-393	485	40	.	.	PUNCT
ejpam-393	486	1	(	(	PUNCT
ejpam-393	486	2	ii	ii	NOUN
ejpam-393	486	3	)	)	PUNCT
ejpam-393	486	4	for	for	ADP
ejpam-393	486	5	a	a	DET
ejpam-393	486	6	given	give	VERB
ejpam-393	486	7	class	class	NOUN
ejpam-393	486	8	m	m	NOUN
ejpam-393	486	9	⊆	⊆	NUM
ejpam-393	486	10	rscm	rscm	NOUN
ejpam-393	486	11	,	,	PUNCT
ejpam-393	486	12	we	we	PRON
ejpam-393	486	13	let	let	VERB
ejpam-393	486	14	nrnm	nrnm	NOUN
ejpam-393	486	15	denote	denote	VERB
ejpam-393	486	16	the	the	DET
ejpam-393	486	17	class	class	NOUN
ejpam-393	486	18	obtained	obtain	VERB
ejpam-393	486	19	by	by	ADP
ejpam-393	486	20	forming	form	VERB
ejpam-393	486	21	the	the	DET
ejpam-393	486	22	neat	neat	ADJ
ejpam-393	486	23	n	n	NOUN
ejpam-393	486	24	-	-	PUNCT
ejpam-393	486	25	reduct	reduct	NOUN
ejpam-393	486	26	of	of	ADP
ejpam-393	486	27	algebras	algebras	PROPN
ejpam-393	486	28	in	in	ADP
ejpam-393	486	29	m	m	PROPN
ejpam-393	486	30	,	,	PUNCT
ejpam-393	486	31	that	that	PRON
ejpam-393	486	32	is	be	AUX
ejpam-393	486	33	nrnm	nrnm	ADJ
ejpam-393	486	34	=	=	PUNCT
ejpam-393	486	35	{	{	PUNCT
ejpam-393	486	36	nrnb	nrnb	NOUN
ejpam-393	486	37	:	:	PUNCT
ejpam-393	486	38	b	b	X
ejpam-393	486	39	∈m	∈m	NOUN
ejpam-393	486	40	}	}	PUNCT
ejpam-393	486	41	.	.	PUNCT
ejpam-393	487	1	the	the	DET
ejpam-393	487	2	definition	definition	NOUN
ejpam-393	487	3	of	of	ADP
ejpam-393	487	4	neat	neat	ADJ
ejpam-393	487	5	reducts	reduct	NOUN
ejpam-393	487	6	for	for	ADP
ejpam-393	487	7	scm	scm	PROPN
ejpam-393	487	8	is	be	AUX
ejpam-393	487	9	the	the	DET
ejpam-393	487	10	same	same	ADJ
ejpam-393	487	11	.	.	PUNCT
ejpam-393	488	1	t.	t.	PROPN
ejpam-393	488	2	ahmed	ahmed	PROPN
ejpam-393	488	3	/	/	SYM
ejpam-393	488	4	eur	eur	PROPN
ejpam-393	488	5	.	.	PUNCT
ejpam-393	489	1	j.	j.	PROPN
ejpam-393	489	2	pure	pure	PROPN
ejpam-393	489	3	appl	appl	PROPN
ejpam-393	489	4	.	.	PROPN
ejpam-393	489	5	math	math	PROPN
ejpam-393	489	6	,	,	PUNCT
ejpam-393	489	7	3	3	NUM
ejpam-393	489	8	(	(	PUNCT
ejpam-393	489	9	2010	2010	NUM
ejpam-393	489	10	)	)	PUNCT
ejpam-393	489	11	,	,	PUNCT
ejpam-393	489	12	853	853	NUM
ejpam-393	489	13	-	-	SYM
ejpam-393	489	14	880	880	NUM
ejpam-393	489	15	863	863	NUM
ejpam-393	489	16	we	we	PRON
ejpam-393	489	17	now	now	ADV
ejpam-393	489	18	prove	prove	VERB
ejpam-393	489	19	:	:	PUNCT
ejpam-393	489	20	theorem	theorem	NOUN
ejpam-393	489	21	5	5	NUM
ejpam-393	489	22	.	.	PUNCT
ejpam-393	490	1	let	let	VERB
ejpam-393	490	2	1	1	NUM
ejpam-393	490	3	<	<	X
ejpam-393	490	4	n	n	NOUN
ejpam-393	490	5	and	and	CCONJ
ejpam-393	490	6	n+	n+	NUM
ejpam-393	490	7	1	1	NUM
ejpam-393	490	8	<	<	X
ejpam-393	490	9	m≤ω	m≤ω	NOUN
ejpam-393	490	10	.	.	PUNCT
ejpam-393	491	1	then	then	ADV
ejpam-393	491	2	nrnrscm	nrnrscm	PROPN
ejpam-393	491	3	and	and	CCONJ
ejpam-393	491	4	nrnscm	nrnscm	PROPN
ejpam-393	491	5	are	be	AUX
ejpam-393	491	6	not	not	PART
ejpam-393	491	7	elementary	elementary	ADJ
ejpam-393	491	8	.	.	PUNCT
ejpam-393	492	1	we	we	PRON
ejpam-393	492	2	do	do	AUX
ejpam-393	492	3	not	not	PART
ejpam-393	492	4	know	know	VERB
ejpam-393	492	5	whether	whether	SCONJ
ejpam-393	492	6	nrnłn+1	nrnłn+1	ADJ
ejpam-393	492	7	for	for	ADP
ejpam-393	492	8	ł	ł	PROPN
ejpam-393	492	9	∈	∈	PROPN
ejpam-393	492	10	{	{	PUNCT
ejpam-393	492	11	sc	sc	PROPN
ejpam-393	492	12	,	,	PUNCT
ejpam-393	492	13	rsc	rsc	PROPN
ejpam-393	492	14	}	}	PUNCT
ejpam-393	492	15	is	be	AUX
ejpam-393	492	16	elementary	elementary	ADJ
ejpam-393	492	17	or	or	CCONJ
ejpam-393	492	18	not	not	PART
ejpam-393	492	19	.	.	PUNCT
ejpam-393	493	1	but	but	CCONJ
ejpam-393	493	2	why	why	SCONJ
ejpam-393	493	3	is	be	AUX
ejpam-393	493	4	it	it	PRON
ejpam-393	493	5	of	of	ADP
ejpam-393	493	6	interest	interest	NOUN
ejpam-393	493	7	to	to	PART
ejpam-393	493	8	settle	settle	VERB
ejpam-393	493	9	such	such	ADJ
ejpam-393	493	10	questions	question	NOUN
ejpam-393	493	11	on	on	ADP
ejpam-393	493	12	neat	neat	ADJ
ejpam-393	493	13	reducts	reduct	NOUN
ejpam-393	493	14	.	.	PUNCT
ejpam-393	494	1	there	there	PRON
ejpam-393	494	2	are	be	VERB
ejpam-393	494	3	(	(	PUNCT
ejpam-393	494	4	at	at	ADP
ejpam-393	494	5	least	least	ADJ
ejpam-393	494	6	)	)	PUNCT
ejpam-393	494	7	three	three	NUM
ejpam-393	494	8	possible	possible	ADJ
ejpam-393	494	9	answers	answer	NOUN
ejpam-393	494	10	to	to	ADP
ejpam-393	494	11	this	this	DET
ejpam-393	494	12	question	question	NOUN
ejpam-393	494	13	.	.	PUNCT
ejpam-393	495	1	first	first	ADV
ejpam-393	495	2	there	there	PRON
ejpam-393	495	3	are	be	VERB
ejpam-393	495	4	aesthetic	aesthetic	ADJ
ejpam-393	495	5	reasons	reason	NOUN
ejpam-393	495	6	.	.	PUNCT
ejpam-393	496	1	motivated	motivate	VERB
ejpam-393	496	2	by	by	ADP
ejpam-393	496	3	intellectual	intellectual	ADJ
ejpam-393	496	4	curiosity	curiosity	NOUN
ejpam-393	496	5	,	,	PUNCT
ejpam-393	496	6	the	the	DET
ejpam-393	496	7	investigation	investigation	NOUN
ejpam-393	496	8	of	of	ADP
ejpam-393	496	9	such	such	ADJ
ejpam-393	496	10	questions	question	NOUN
ejpam-393	496	11	is	be	AUX
ejpam-393	496	12	likely	likely	ADJ
ejpam-393	496	13	to	to	PART
ejpam-393	496	14	lead	lead	VERB
ejpam-393	496	15	to	to	ADP
ejpam-393	496	16	nice	nice	ADJ
ejpam-393	496	17	mathematics	mathematic	NOUN
ejpam-393	496	18	.	.	PUNCT
ejpam-393	497	1	the	the	DET
ejpam-393	497	2	second	second	ADJ
ejpam-393	497	3	reason	reason	NOUN
ejpam-393	497	4	concerns	concern	VERB
ejpam-393	497	5	definability	definability	NOUN
ejpam-393	497	6	or	or	CCONJ
ejpam-393	497	7	classification	classification	NOUN
ejpam-393	497	8	.	.	PUNCT
ejpam-393	498	1	now	now	ADV
ejpam-393	498	2	that	that	SCONJ
ejpam-393	498	3	we	we	PRON
ejpam-393	498	4	have	have	VERB
ejpam-393	498	5	the	the	DET
ejpam-393	498	6	class	class	NOUN
ejpam-393	498	7	of	of	ADP
ejpam-393	498	8	neat	neat	ADJ
ejpam-393	498	9	reducts	reduct	NOUN
ejpam-393	498	10	in	in	ADP
ejpam-393	498	11	front	front	NOUN
ejpam-393	498	12	of	of	ADP
ejpam-393	498	13	us	we	PRON
ejpam-393	498	14	,	,	PUNCT
ejpam-393	498	15	the	the	DET
ejpam-393	498	16	most	most	ADV
ejpam-393	498	17	pressing	pressing	ADJ
ejpam-393	498	18	need	need	NOUN
ejpam-393	498	19	is	be	AUX
ejpam-393	498	20	to	to	PART
ejpam-393	498	21	try	try	VERB
ejpam-393	498	22	to	to	PART
ejpam-393	498	23	classify	classify	VERB
ejpam-393	498	24	it	it	PRON
ejpam-393	498	25	.	.	PUNCT
ejpam-393	499	1	classifying	classify	VERB
ejpam-393	499	2	is	be	AUX
ejpam-393	499	3	a	a	DET
ejpam-393	499	4	kind	kind	NOUN
ejpam-393	499	5	of	of	ADP
ejpam-393	499	6	defining	define	VERB
ejpam-393	499	7	.	.	PUNCT
ejpam-393	500	1	most	most	ADJ
ejpam-393	500	2	mathematical	mathematical	ADJ
ejpam-393	500	3	classification	classification	NOUN
ejpam-393	500	4	is	be	AUX
ejpam-393	500	5	by	by	ADP
ejpam-393	500	6	axioms	axiom	NOUN
ejpam-393	500	7	(	(	PUNCT
ejpam-393	500	8	preferably	preferably	ADV
ejpam-393	500	9	first	first	ADJ
ejpam-393	500	10	order	order	NOUN
ejpam-393	500	11	)	)	PUNCT
ejpam-393	500	12	or	or	CCONJ
ejpam-393	500	13	,	,	PUNCT
ejpam-393	500	14	even	even	ADV
ejpam-393	500	15	better	well	ADJ
ejpam-393	500	16	,	,	PUNCT
ejpam-393	500	17	equations	equation	NOUN
ejpam-393	500	18	(	(	PUNCT
ejpam-393	500	19	if	if	SCONJ
ejpam-393	500	20	the	the	DET
ejpam-393	500	21	class	class	NOUN
ejpam-393	500	22	in	in	ADP
ejpam-393	500	23	question	question	NOUN
ejpam-393	500	24	is	be	AUX
ejpam-393	500	25	a	a	DET
ejpam-393	500	26	variety	variety	NOUN
ejpam-393	500	27	.	.	PUNCT
ejpam-393	500	28	)	)	PUNCT
ejpam-393	501	1	it	it	PRON
ejpam-393	501	2	is	be	AUX
ejpam-393	501	3	known	know	VERB
ejpam-393	501	4	(	(	PUNCT
ejpam-393	501	5	and	and	CCONJ
ejpam-393	501	6	indeed	indeed	ADV
ejpam-393	501	7	not	not	PART
ejpam-393	501	8	difficult	difficult	ADJ
ejpam-393	501	9	to	to	PART
ejpam-393	501	10	show	show	VERB
ejpam-393	501	11	)	)	PUNCT
ejpam-393	501	12	that	that	SCONJ
ejpam-393	501	13	the	the	DET
ejpam-393	501	14	class	class	NOUN
ejpam-393	501	15	nrncam	nrncam	NOUN
ejpam-393	501	16	is	be	AUX
ejpam-393	501	17	closed	close	VERB
ejpam-393	501	18	under	under	ADP
ejpam-393	501	19	products	product	NOUN
ejpam-393	501	20	and	and	CCONJ
ejpam-393	501	21	homomorphic	homomorphic	ADJ
ejpam-393	501	22	images	image	NOUN
ejpam-393	501	23	for	for	ADP
ejpam-393	501	24	all	all	DET
ejpam-393	501	25	n	n	CCONJ
ejpam-393	501	26	<	<	X
ejpam-393	501	27	m	m	PROPN
ejpam-393	502	1	[	[	X
ejpam-393	502	2	45	45	NUM
ejpam-393	502	3	]	]	PUNCT
ejpam-393	502	4	.	.	PUNCT
ejpam-393	503	1	however	however	ADV
ejpam-393	503	2	,	,	PUNCT
ejpam-393	503	3	it	it	PRON
ejpam-393	503	4	is	be	AUX
ejpam-393	503	5	not	not	PART
ejpam-393	503	6	closed	close	VERB
ejpam-393	503	7	under	under	ADP
ejpam-393	503	8	forming	form	VERB
ejpam-393	503	9	(	(	PUNCT
ejpam-393	503	10	elementary	elementary	ADJ
ejpam-393	503	11	)	)	PUNCT
ejpam-393	503	12	subalgebras	subalgebras	PROPN
ejpam-393	504	1	[	[	X
ejpam-393	504	2	18	18	NUM
ejpam-393	504	3	]	]	X
ejpam-393	504	4	,	,	PUNCT
ejpam-393	504	5	that	that	ADV
ejpam-393	504	6	is	is	ADV
ejpam-393	504	7	,	,	PUNCT
ejpam-393	504	8	it	it	PRON
ejpam-393	504	9	is	be	AUX
ejpam-393	504	10	not	not	PART
ejpam-393	504	11	axiomatizable	axiomatizable	ADJ
ejpam-393	504	12	,	,	PUNCT
ejpam-393	504	13	a	a	DET
ejpam-393	504	14	priori	priori	ADJ
ejpam-393	504	15	not	not	PART
ejpam-393	504	16	a	a	DET
ejpam-393	504	17	variety	variety	NOUN
ejpam-393	504	18	.	.	PUNCT
ejpam-393	505	1	studying	study	VERB
ejpam-393	505	2	neat	neat	ADJ
ejpam-393	505	3	reducts	reduct	NOUN
ejpam-393	505	4	of	of	ADP
ejpam-393	505	5	reducts	reduct	NOUN
ejpam-393	505	6	of	of	ADP
ejpam-393	505	7	ca	ca	NOUN
ejpam-393	505	8	’s	’s	X
ejpam-393	505	9	and	and	CCONJ
ejpam-393	505	10	for	for	ADP
ejpam-393	505	11	that	that	DET
ejpam-393	505	12	matter	matter	NOUN
ejpam-393	505	13	expansions	expansion	NOUN
ejpam-393	505	14	[	[	X
ejpam-393	505	15	34	34	NUM
ejpam-393	505	16	]	]	PUNCT
ejpam-393	505	17	,	,	PUNCT
ejpam-393	505	18	[	[	X
ejpam-393	505	19	29	29	NUM
ejpam-393	505	20	]	]	PUNCT
ejpam-393	505	21	,	,	PUNCT
ejpam-393	505	22	clarifies	clarify	VERB
ejpam-393	505	23	the	the	DET
ejpam-393	505	24	properties	property	NOUN
ejpam-393	505	25	of	of	ADP
ejpam-393	505	26	neat	neat	ADJ
ejpam-393	505	27	reducts	reduct	NOUN
ejpam-393	505	28	.	.	PUNCT
ejpam-393	506	1	(	(	PUNCT
ejpam-393	506	2	this	this	PRON
ejpam-393	506	3	is	be	AUX
ejpam-393	506	4	similar	similar	ADJ
ejpam-393	506	5	to	to	ADP
ejpam-393	506	6	the	the	DET
ejpam-393	506	7	situation	situation	NOUN
ejpam-393	506	8	with	with	ADP
ejpam-393	506	9	representability	representability	NOUN
ejpam-393	506	10	[	[	X
ejpam-393	506	11	15	15	NUM
ejpam-393	506	12	]	]	PUNCT
ejpam-393	506	13	where	where	SCONJ
ejpam-393	506	14	axiomatizations	axiomatization	NOUN
ejpam-393	506	15	of	of	ADP
ejpam-393	506	16	representable	representable	ADJ
ejpam-393	506	17	algebras	algebra	NOUN
ejpam-393	506	18	are	be	AUX
ejpam-393	506	19	better	well	ADV
ejpam-393	506	20	understood	understand	VERB
ejpam-393	506	21	by	by	ADP
ejpam-393	506	22	passing	pass	VERB
ejpam-393	506	23	to	to	ADP
ejpam-393	506	24	reducts	reduct	NOUN
ejpam-393	506	25	or	or	CCONJ
ejpam-393	506	26	expansions	expansion	NOUN
ejpam-393	506	27	.	.	PUNCT
ejpam-393	506	28	)	)	PUNCT
ejpam-393	507	1	now	now	ADV
ejpam-393	507	2	we	we	PRON
ejpam-393	507	3	come	come	VERB
ejpam-393	507	4	to	to	ADP
ejpam-393	507	5	the	the	DET
ejpam-393	507	6	third	third	ADJ
ejpam-393	507	7	reason	reason	NOUN
ejpam-393	507	8	,	,	PUNCT
ejpam-393	507	9	where	where	SCONJ
ejpam-393	507	10	neat	neat	ADJ
ejpam-393	507	11	reducts	reduct	NOUN
ejpam-393	507	12	are	be	AUX
ejpam-393	507	13	not	not	PART
ejpam-393	507	14	treated	treat	VERB
ejpam-393	507	15	on	on	ADP
ejpam-393	507	16	its	its	PRON
ejpam-393	507	17	own	own	ADJ
ejpam-393	507	18	but	but	CCONJ
ejpam-393	507	19	rather	rather	ADV
ejpam-393	507	20	in	in	ADP
ejpam-393	507	21	its	its	PRON
ejpam-393	507	22	interaction	interaction	NOUN
ejpam-393	507	23	with	with	ADP
ejpam-393	507	24	algebraic	algebraic	ADJ
ejpam-393	507	25	properties	property	NOUN
ejpam-393	507	26	like	like	ADP
ejpam-393	507	27	representability	representability	NOUN
ejpam-393	507	28	,	,	PUNCT
ejpam-393	507	29	amalgamation	amalgamation	NOUN
ejpam-393	507	30	and	and	CCONJ
ejpam-393	507	31	complete	complete	ADJ
ejpam-393	507	32	representations	representation	NOUN
ejpam-393	507	33	.	.	PUNCT
ejpam-393	508	1	this	this	PRON
ejpam-393	508	2	in	in	ADP
ejpam-393	508	3	turn	turn	NOUN
ejpam-393	508	4	is	be	AUX
ejpam-393	508	5	related	relate	VERB
ejpam-393	508	6	to	to	ADP
ejpam-393	508	7	completeness	completeness	NOUN
ejpam-393	508	8	,	,	PUNCT
ejpam-393	508	9	interpolation	interpolation	NOUN
ejpam-393	508	10	and	and	CCONJ
ejpam-393	508	11	omittting	omittting	NOUN
ejpam-393	508	12	types	type	NOUN
ejpam-393	508	13	for	for	ADP
ejpam-393	508	14	variants	variant	NOUN
ejpam-393	508	15	of	of	ADP
ejpam-393	508	16	first	first	ADJ
ejpam-393	508	17	order	order	NOUN
ejpam-393	508	18	logic	logic	NOUN
ejpam-393	508	19	,	,	PUNCT
ejpam-393	508	20	be	be	AUX
ejpam-393	508	21	it	it	PRON
ejpam-393	508	22	reducts	reduct	NOUN
ejpam-393	508	23	or	or	CCONJ
ejpam-393	508	24	expansions	expansion	NOUN
ejpam-393	508	25	[	[	X
ejpam-393	508	26	24	24	NUM
ejpam-393	508	27	,	,	PUNCT
ejpam-393	508	28	22	22	NUM
ejpam-393	508	29	]	]	PUNCT
ejpam-393	508	30	,	,	PUNCT
ejpam-393	508	31	[	[	X
ejpam-393	508	32	33	33	NUM
ejpam-393	508	33	]	]	PUNCT
ejpam-393	508	34	.	.	PUNCT
ejpam-393	509	1	indeed	indeed	ADV
ejpam-393	509	2	the	the	DET
ejpam-393	509	3	old	old	ADJ
ejpam-393	509	4	but	but	CCONJ
ejpam-393	509	5	venerable	venerable	ADJ
ejpam-393	509	6	notion	notion	NOUN
ejpam-393	509	7	of	of	ADP
ejpam-393	509	8	neat	neat	ADJ
ejpam-393	509	9	reducts	reduct	NOUN
ejpam-393	509	10	has	have	AUX
ejpam-393	509	11	turned	turn	VERB
ejpam-393	509	12	to	to	PART
ejpam-393	509	13	be	be	AUX
ejpam-393	509	14	central	central	ADJ
ejpam-393	509	15	notion	notion	NOUN
ejpam-393	509	16	in	in	ADP
ejpam-393	509	17	the	the	DET
ejpam-393	509	18	theory	theory	NOUN
ejpam-393	509	19	of	of	ADP
ejpam-393	509	20	cylindric	cylindric	ADJ
ejpam-393	509	21	like	like	ADP
ejpam-393	509	22	algebras	algebra	NOUN
ejpam-393	509	23	of	of	ADP
ejpam-393	509	24	relations	relation	NOUN
ejpam-393	509	25	,	,	PUNCT
ejpam-393	509	26	[	[	X
ejpam-393	509	27	23	23	NUM
ejpam-393	509	28	,	,	PUNCT
ejpam-393	509	29	32	32	NUM
ejpam-393	509	30	,	,	PUNCT
ejpam-393	509	31	30	30	NUM
ejpam-393	509	32	,	,	PUNCT
ejpam-393	509	33	16	16	NUM
ejpam-393	509	34	]	]	PUNCT
ejpam-393	509	35	.	.	PUNCT
ejpam-393	510	1	we	we	PRON
ejpam-393	510	2	shall	shall	AUX
ejpam-393	510	3	need	need	VERB
ejpam-393	510	4	the	the	DET
ejpam-393	510	5	following	follow	VERB
ejpam-393	510	6	lemma	lemma	PROPN
ejpam-393	510	7	on	on	ADP
ejpam-393	510	8	substitutions	substitution	NOUN
ejpam-393	510	9	:	:	PUNCT
ejpam-393	510	10	lemma	lemma	PROPN
ejpam-393	510	11	4	4	X
ejpam-393	510	12	.	.	X
ejpam-393	510	13	for	for	ADP
ejpam-393	510	14	any	any	DET
ejpam-393	510	15	k	k	PROPN
ejpam-393	510	16	,	,	PUNCT
ejpam-393	510	17	l	l	NOUN
ejpam-393	510	18	,	,	PUNCT
ejpam-393	510	19	u	u	NOUN
ejpam-393	510	20	<	<	X
ejpam-393	510	21	n	n	NOUN
ejpam-393	510	22	and	and	CCONJ
ejpam-393	510	23	a	a	DET
ejpam-393	510	24	∈	∈	NOUN
ejpam-393	510	25	rscn	rscn	NOUN
ejpam-393	510	26	,	,	PUNCT
ejpam-393	510	27	set	set	VERB
ejpam-393	510	28	us(k	us(k	ADP
ejpam-393	510	29	,	,	PUNCT
ejpam-393	510	30	l)x	l)x	X
ejpam-393	511	1	=	=	SYM
ejpam-393	511	2	su	su	PROPN
ejpam-393	511	3	k	k	PROPN
ejpam-393	511	4	sk	sk	PROPN
ejpam-393	511	5	l	l	PROPN
ejpam-393	511	6	s	s	PART
ejpam-393	511	7	l	l	NOUN
ejpam-393	511	8	u	u	NOUN
ejpam-393	511	9	x	x	X
ejpam-393	511	10	.	.	PUNCT
ejpam-393	512	1	then	then	ADV
ejpam-393	512	2	(	(	PUNCT
ejpam-393	512	3	i	i	NOUN
ejpam-393	512	4	)	)	PUNCT
ejpam-393	512	5	if	if	SCONJ
ejpam-393	512	6	k	k	X
ejpam-393	512	7	,	,	PUNCT
ejpam-393	512	8	l	l	NOUN
ejpam-393	512	9	,	,	PUNCT
ejpam-393	512	10	u	u	NOUN
ejpam-393	512	11	and	and	CCONJ
ejpam-393	512	12	v	v	NOUN
ejpam-393	512	13	are	be	AUX
ejpam-393	512	14	distinct	distinct	ADJ
ejpam-393	512	15	,	,	PUNCT
ejpam-393	512	16	then	then	ADV
ejpam-393	512	17	us(k	us(k	X
ejpam-393	512	18	,	,	PUNCT
ejpam-393	512	19	l)cucv	l)cucv	NOUN
ejpam-393	512	20	x	x	SYM
ejpam-393	512	21	=	=	SYM
ejpam-393	512	22	us(l	us(l	PROPN
ejpam-393	512	23	,	,	PUNCT
ejpam-393	512	24	k)cucv	k)cucv	PROPN
ejpam-393	512	25	x	x	SYM
ejpam-393	512	26	(	(	PUNCT
ejpam-393	512	27	ii	ii	NOUN
ejpam-393	512	28	)	)	PUNCT
ejpam-393	512	29	with	with	ADP
ejpam-393	512	30	the	the	DET
ejpam-393	512	31	same	same	ADJ
ejpam-393	512	32	condition	condition	NOUN
ejpam-393	512	33	in	in	ADP
ejpam-393	512	34	(	(	PUNCT
ejpam-393	512	35	i	i	NOUN
ejpam-393	512	36	)	)	PUNCT
ejpam-393	512	37	,	,	PUNCT
ejpam-393	512	38	we	we	PRON
ejpam-393	512	39	have	have	VERB
ejpam-393	512	40	us(k	us(k	NOUN
ejpam-393	512	41	,	,	PUNCT
ejpam-393	512	42	l)us(k	l)us(k	ADJ
ejpam-393	512	43	,	,	PUNCT
ejpam-393	512	44	l)cucv	l)cucv	NOUN
ejpam-393	512	45	x	x	SYM
ejpam-393	512	46	=	=	SYM
ejpam-393	512	47	cucv	cucv	NOUN
ejpam-393	512	48	x	x	X
ejpam-393	512	49	.	.	PUNCT
ejpam-393	513	1	the	the	DET
ejpam-393	513	2	proof	proof	NOUN
ejpam-393	513	3	is	be	AUX
ejpam-393	513	4	tedious	tedious	ADJ
ejpam-393	513	5	,	,	PUNCT
ejpam-393	513	6	but	but	CCONJ
ejpam-393	513	7	fairly	fairly	ADV
ejpam-393	513	8	straight	straight	ADV
ejpam-393	513	9	forward	forward	ADV
ejpam-393	513	10	.	.	PUNCT
ejpam-393	514	1	we	we	PRON
ejpam-393	514	2	use	use	VERB
ejpam-393	514	3	the	the	DET
ejpam-393	514	4	axiomatization	axiomatization	NOUN
ejpam-393	514	5	(	(	PUNCT
ejpam-393	514	6	e1	e1	PROPN
ejpam-393	514	7	−	−	PROPN
ejpam-393	514	8	e9	e9	PROPN
ejpam-393	514	9	)	)	PUNCT
ejpam-393	514	10	.	.	PUNCT
ejpam-393	515	1	proof	proof	NOUN
ejpam-393	515	2	.	.	PUNCT
ejpam-393	516	1	sl	sl	VERB
ejpam-393	516	2	us	we	PRON
ejpam-393	516	3	u	u	NOUN
ejpam-393	516	4	k	k	PROPN
ejpam-393	516	5	sk	sk	PROPN
ejpam-393	516	6	l	l	NOUN
ejpam-393	516	7	sl	sl	NOUN
ejpam-393	516	8	ucucv	ucucv	NOUN
ejpam-393	516	9	x	x	PUNCT
ejpam-393	517	1	=	=	PUNCT
ejpam-393	517	2	(	(	PUNCT
ejpam-393	517	3	by	by	ADP
ejpam-393	517	4	e8	e8	PROPN
ejpam-393	517	5	)	)	PUNCT
ejpam-393	517	6	sl	sl	VERB
ejpam-393	517	7	us	we	PRON
ejpam-393	517	8	u	u	NOUN
ejpam-393	517	9	k	k	PROPN
ejpam-393	517	10	sk	sk	PROPN
ejpam-393	517	11	l	l	PROPN
ejpam-393	517	12	sv	sv	ADP
ejpam-393	517	13	us	us	PROPN
ejpam-393	518	1	l	l	PROPN
ejpam-393	518	2	vcvcu	vcvcu	ADJ
ejpam-393	518	3	x	x	X
ejpam-393	518	4	=	=	PUNCT
ejpam-393	518	5	(	(	PUNCT
ejpam-393	518	6	by	by	ADP
ejpam-393	518	7	e9	e9	PROPN
ejpam-393	518	8	)	)	PUNCT
ejpam-393	518	9	sl	sl	VERB
ejpam-393	518	10	us	we	PRON
ejpam-393	518	11	u	u	INTJ
ejpam-393	518	12	ks	ks	PROPN
ejpam-393	518	13	v	v	ADP
ejpam-393	518	14	us	we	PRON
ejpam-393	518	15	k	k	PROPN
ejpam-393	518	16	l	l	PROPN
ejpam-393	518	17	s	s	PART
ejpam-393	518	18	l	l	NOUN
ejpam-393	518	19	vcucv	vcucv	X
ejpam-393	518	20	x	x	X
ejpam-393	518	21	(	(	PUNCT
ejpam-393	518	22	by	by	ADP
ejpam-393	518	23	e6	e6	NOUN
ejpam-393	518	24	)	)	PUNCT
ejpam-393	518	25	=	=	PUNCT
ejpam-393	519	1	sl	sl	VERB
ejpam-393	519	2	us	we	PRON
ejpam-393	519	3	u	u	INTJ
ejpam-393	519	4	ks	ks	PROPN
ejpam-393	519	5	v	v	ADP
ejpam-393	519	6	us	we	PRON
ejpam-393	519	7	k	k	PROPN
ejpam-393	519	8	l	l	PROPN
ejpam-393	519	9	cus	cus	PROPN
ejpam-393	519	10	l	l	NOUN
ejpam-393	519	11	vcv	vcv	NOUN
ejpam-393	519	12	x	x	X
ejpam-393	519	13	(	(	PUNCT
ejpam-393	519	14	by	by	ADP
ejpam-393	519	15	e6	e6	NOUN
ejpam-393	519	16	)	)	PUNCT
ejpam-393	520	1	=	=	PUNCT
ejpam-393	520	2	sl	sl	VERB
ejpam-393	520	3	us	we	PRON
ejpam-393	520	4	u	u	INTJ
ejpam-393	520	5	ks	ks	PROPN
ejpam-393	520	6	v	v	NUM
ejpam-393	520	7	ucus	ucus	NOUN
ejpam-393	520	8	k	k	PROPN
ejpam-393	520	9	l	l	PROPN
ejpam-393	520	10	s	s	PART
ejpam-393	520	11	l	l	NOUN
ejpam-393	520	12	vcv	vcv	NOUN
ejpam-393	520	13	x	x	PUNCT
ejpam-393	520	14	=	=	PUNCT
ejpam-393	520	15	(	(	PUNCT
ejpam-393	520	16	by	by	ADP
ejpam-393	520	17	e8	e8	PROPN
ejpam-393	520	18	)	)	PUNCT
ejpam-393	520	19	sl	sl	VERB
ejpam-393	520	20	us	we	PRON
ejpam-393	520	21	v	v	ADP
ejpam-393	520	22	kcus	kcus	PROPN
ejpam-393	520	23	k	k	PROPN
ejpam-393	520	24	l	l	PROPN
ejpam-393	520	25	s	s	PART
ejpam-393	520	26	l	l	NOUN
ejpam-393	520	27	vcucv	vcucv	X
ejpam-393	520	28	x	x	PUNCT
ejpam-393	520	29	.	.	PUNCT
ejpam-393	521	1	t.	t.	PROPN
ejpam-393	521	2	ahmed	ahmed	PROPN
ejpam-393	521	3	/	/	SYM
ejpam-393	521	4	eur	eur	PROPN
ejpam-393	521	5	.	.	PUNCT
ejpam-393	522	1	j.	j.	PROPN
ejpam-393	522	2	pure	pure	PROPN
ejpam-393	522	3	appl	appl	PROPN
ejpam-393	522	4	.	.	PROPN
ejpam-393	522	5	math	math	PROPN
ejpam-393	522	6	,	,	PUNCT
ejpam-393	522	7	3	3	NUM
ejpam-393	522	8	(	(	PUNCT
ejpam-393	522	9	2010	2010	NUM
ejpam-393	522	10	)	)	PUNCT
ejpam-393	522	11	,	,	PUNCT
ejpam-393	522	12	853	853	NUM
ejpam-393	522	13	-	-	SYM
ejpam-393	522	14	880	880	NUM
ejpam-393	522	15	864	864	NUM
ejpam-393	522	16	now	now	ADV
ejpam-393	522	17	sl	sl	VERB
ejpam-393	522	18	us	we	PRON
ejpam-393	522	19	v	v	ADP
ejpam-393	522	20	kcus	kcus	PROPN
ejpam-393	522	21	k	k	PROPN
ejpam-393	522	22	l	l	PROPN
ejpam-393	522	23	s	s	PART
ejpam-393	522	24	l	l	X
ejpam-393	522	25	vcucv	vcucv	X
ejpam-393	522	26	x	x	X
ejpam-393	522	27	(	(	PUNCT
ejpam-393	522	28	by	by	ADP
ejpam-393	522	29	e8	e8	PROPN
ejpam-393	522	30	)	)	PUNCT
ejpam-393	523	1	=	=	PUNCT
ejpam-393	523	2	sl	sl	VERB
ejpam-393	523	3	us	we	PRON
ejpam-393	523	4	v	v	ADP
ejpam-393	523	5	ks	ks	PROPN
ejpam-393	523	6	k	k	PROPN
ejpam-393	523	7	l	l	PROPN
ejpam-393	523	8	s	s	PART
ejpam-393	523	9	l	l	NOUN
ejpam-393	523	10	vcucv	vcucv	X
ejpam-393	523	11	x	x	PUNCT
ejpam-393	523	12	=	=	PUNCT
ejpam-393	523	13	(	(	PUNCT
ejpam-393	523	14	by	by	ADP
ejpam-393	523	15	e9	e9	NOUN
ejpam-393	523	16	)	)	PUNCT
ejpam-393	523	17	sv	sv	PROPN
ejpam-393	524	1	ks	ks	PROPN
ejpam-393	524	2	l	l	PROPN
ejpam-393	524	3	us	we	PRON
ejpam-393	525	1	k	k	PROPN
ejpam-393	525	2	l	l	PROPN
ejpam-393	525	3	s	s	PART
ejpam-393	525	4	l	l	NOUN
ejpam-393	525	5	vcucv	vcucv	X
ejpam-393	525	6	x	x	PUNCT
ejpam-393	525	7	=	=	PUNCT
ejpam-393	525	8	(	(	PUNCT
ejpam-393	525	9	by	by	ADP
ejpam-393	525	10	e5	e5	PROPN
ejpam-393	525	11	)	)	PUNCT
ejpam-393	525	12	sv	sv	PROPN
ejpam-393	526	1	ks	ks	PROPN
ejpam-393	526	2	l	l	PROPN
ejpam-393	526	3	us	us	PROPN
ejpam-393	527	1	k	k	PROPN
ejpam-393	527	2	l	l	PROPN
ejpam-393	527	3	cls	cls	NOUN
ejpam-393	527	4	l	l	PROPN
ejpam-393	527	5	vcucv	vcucv	X
ejpam-393	527	6	x	x	PUNCT
ejpam-393	527	7	=	=	SYM
ejpam-393	527	8	(	(	PUNCT
ejpam-393	527	9	by	by	ADP
ejpam-393	527	10	e8	e8	PROPN
ejpam-393	527	11	)	)	PUNCT
ejpam-393	527	12	sv	sv	PROPN
ejpam-393	527	13	ks	ks	PROPN
ejpam-393	527	14	k	k	PROPN
ejpam-393	527	15	ucls	ucls	PROPN
ejpam-393	527	16	l	l	PROPN
ejpam-393	527	17	vcucv	vcucv	X
ejpam-393	527	18	x	x	PUNCT
ejpam-393	527	19	=	=	PUNCT
ejpam-393	527	20	(	(	PUNCT
ejpam-393	527	21	by	by	ADP
ejpam-393	527	22	e5	e5	PROPN
ejpam-393	527	23	)	)	PUNCT
ejpam-393	527	24	sv	sv	PROPN
ejpam-393	528	1	ks	ks	PROPN
ejpam-393	528	2	k	k	PROPN
ejpam-393	528	3	us	us	PROPN
ejpam-393	528	4	l	l	PROPN
ejpam-393	528	5	vcucv	vcucv	X
ejpam-393	528	6	x	x	X
ejpam-393	528	7	(	(	PUNCT
ejpam-393	528	8	by	by	ADP
ejpam-393	528	9	e9	e9	NOUN
ejpam-393	528	10	)	)	PUNCT
ejpam-393	528	11	=	=	SYM
ejpam-393	528	12	sv	sv	PROPN
ejpam-393	528	13	ks	ks	PROPN
ejpam-393	528	14	l	l	PROPN
ejpam-393	528	15	vs	vs	ADP
ejpam-393	528	16	k	k	PROPN
ejpam-393	528	17	ucucv	ucucv	NOUN
ejpam-393	528	18	x	x	PUNCT
ejpam-393	529	1	=	=	PUNCT
ejpam-393	529	2	(	(	PUNCT
ejpam-393	529	3	by	by	ADP
ejpam-393	529	4	e6	e6	PROPN
ejpam-393	529	5	)	)	PUNCT
ejpam-393	529	6	sv	sv	PROPN
ejpam-393	529	7	ks	ks	PROPN
ejpam-393	529	8	l	l	PROPN
ejpam-393	529	9	vcvs	vcvs	PROPN
ejpam-393	529	10	k	k	PROPN
ejpam-393	529	11	ucu	ucu	PROPN
ejpam-393	529	12	x	x	PROPN
ejpam-393	530	1	=	=	PUNCT
ejpam-393	530	2	(	(	PUNCT
ejpam-393	530	3	by	by	ADP
ejpam-393	530	4	e8	e8	PROPN
ejpam-393	530	5	)	)	PUNCT
ejpam-393	530	6	sl	sl	PROPN
ejpam-393	530	7	ks	ks	PROPN
ejpam-393	530	8	k	k	PROPN
ejpam-393	530	9	ucucv	ucucv	PROPN
ejpam-393	530	10	x	x	X
ejpam-393	530	11	.	.	PUNCT
ejpam-393	531	1	we	we	PRON
ejpam-393	531	2	have	have	AUX
ejpam-393	531	3	proved	prove	VERB
ejpam-393	531	4	that	that	SCONJ
ejpam-393	531	5	sl	sl	VERB
ejpam-393	531	6	us	we	PRON
ejpam-393	532	1	u	u	NOUN
ejpam-393	533	1	k	k	PROPN
ejpam-393	534	1	sk	sk	PROPN
ejpam-393	534	2	l	l	PROPN
ejpam-393	534	3	s	s	PART
ejpam-393	534	4	l	l	NOUN
ejpam-393	534	5	ucucv	ucucv	NOUN
ejpam-393	534	6	x	x	PUNCT
ejpam-393	535	1	=	=	PUNCT
ejpam-393	535	2	sl	sl	INTJ
ejpam-393	535	3	k	k	NOUN
ejpam-393	535	4	sk	sk	X
ejpam-393	535	5	ucucv	ucucv	NOUN
ejpam-393	535	6	x	x	X
ejpam-393	535	7	.	.	PUNCT
ejpam-393	536	1	now	now	ADV
ejpam-393	536	2	we	we	PRON
ejpam-393	536	3	apply	apply	VERB
ejpam-393	536	4	su	su	PROPN
ejpam-393	536	5	l	l	NOUN
ejpam-393	536	6	to	to	ADP
ejpam-393	536	7	both	both	DET
ejpam-393	536	8	sides	side	NOUN
ejpam-393	536	9	,	,	PUNCT
ejpam-393	536	10	we	we	PRON
ejpam-393	536	11	obtain	obtain	VERB
ejpam-393	536	12	,	,	PUNCT
ejpam-393	536	13	the	the	DET
ejpam-393	536	14	right	right	ADJ
ejpam-393	536	15	hand	hand	NOUN
ejpam-393	536	16	side	side	NOUN
ejpam-393	536	17	is	be	AUX
ejpam-393	536	18	equal	equal	ADJ
ejpam-393	536	19	to	to	ADP
ejpam-393	536	20	su	su	PROPN
ejpam-393	536	21	l	l	NOUN
ejpam-393	537	1	sl	sl	VERB
ejpam-393	537	2	us	we	PRON
ejpam-393	537	3	u	u	NOUN
ejpam-393	537	4	k	k	PROPN
ejpam-393	537	5	sk	sk	PROPN
ejpam-393	537	6	l	l	NOUN
ejpam-393	537	7	sl	sl	NOUN
ejpam-393	537	8	ucucv	ucucv	NOUN
ejpam-393	537	9	x	x	PUNCT
ejpam-393	538	1	=	=	PUNCT
ejpam-393	538	2	(	(	PUNCT
ejpam-393	538	3	by	by	ADP
ejpam-393	538	4	e5	e5	PROPN
ejpam-393	538	5	)	)	PUNCT
ejpam-393	538	6	su	su	PROPN
ejpam-393	538	7	l	l	PROPN
ejpam-393	538	8	sl	sl	NOUN
ejpam-393	538	9	ucus	ucus	NOUN
ejpam-393	538	10	u	u	NOUN
ejpam-393	538	11	k	k	PROPN
ejpam-393	538	12	sk	sk	PROPN
ejpam-393	538	13	l	l	NOUN
ejpam-393	538	14	sl	sl	NOUN
ejpam-393	538	15	ucucv	ucucv	NOUN
ejpam-393	538	16	x	x	PUNCT
ejpam-393	538	17	=	=	PUNCT
ejpam-393	538	18	(	(	PUNCT
ejpam-393	538	19	by	by	ADP
ejpam-393	538	20	e8	e8	PROPN
ejpam-393	538	21	)	)	PUNCT
ejpam-393	538	22	sl	sl	PROPN
ejpam-393	538	23	l	l	NOUN
ejpam-393	538	24	cus	cus	PROPN
ejpam-393	538	25	u	u	PROPN
ejpam-393	538	26	k	k	PROPN
ejpam-393	538	27	sk	sk	PROPN
ejpam-393	538	28	l	l	NOUN
ejpam-393	538	29	sl	sl	NOUN
ejpam-393	538	30	ucucv	ucucv	NOUN
ejpam-393	538	31	x	x	PUNCT
ejpam-393	539	1	=	=	PUNCT
ejpam-393	539	2	(	(	PUNCT
ejpam-393	539	3	by	by	ADP
ejpam-393	539	4	e5	e5	PROPN
ejpam-393	539	5	)	)	PUNCT
ejpam-393	539	6	su	su	PROPN
ejpam-393	540	1	k	k	PROPN
ejpam-393	540	2	sk	sk	PROPN
ejpam-393	540	3	l	l	NOUN
ejpam-393	540	4	sl	sl	NOUN
ejpam-393	540	5	ucucv	ucucv	NOUN
ejpam-393	540	6	x	x	PUNCT
ejpam-393	541	1	=	=	PUNCT
ejpam-393	541	2	us(k	us(k	NOUN
ejpam-393	541	3	,	,	PUNCT
ejpam-393	541	4	l)cucv	l)cucv	NOUN
ejpam-393	541	5	x	x	X
ejpam-393	541	6	and	and	CCONJ
ejpam-393	541	7	by	by	ADP
ejpam-393	541	8	definition	definition	NOUN
ejpam-393	541	9	the	the	DET
ejpam-393	541	10	left	left	ADJ
ejpam-393	541	11	hand	hand	NOUN
ejpam-393	541	12	side	side	NOUN
ejpam-393	541	13	is	be	AUX
ejpam-393	541	14	equal	equal	ADJ
ejpam-393	541	15	to	to	ADP
ejpam-393	541	16	us(l	us(l	NUM
ejpam-393	541	17	,	,	PUNCT
ejpam-393	541	18	k)cucv	k)cucv	PROPN
ejpam-393	541	19	x	x	PUNCT
ejpam-393	541	20	.	.	PUNCT
ejpam-393	542	1	we	we	PRON
ejpam-393	542	2	have	have	AUX
ejpam-393	542	3	proved	prove	VERB
ejpam-393	542	4	(	(	PUNCT
ejpam-393	542	5	i	i	NOUN
ejpam-393	542	6	)	)	PUNCT
ejpam-393	542	7	.	.	PUNCT
ejpam-393	543	1	we	we	PRON
ejpam-393	543	2	now	now	ADV
ejpam-393	543	3	prove	prove	VERB
ejpam-393	543	4	(	(	PUNCT
ejpam-393	543	5	ii	ii	NOUN
ejpam-393	543	6	)	)	PUNCT
ejpam-393	543	7	.	.	PUNCT
ejpam-393	544	1	from	from	ADP
ejpam-393	544	2	(	(	PUNCT
ejpam-393	544	3	i	i	NOUN
ejpam-393	544	4	)	)	PUNCT
ejpam-393	544	5	we	we	PRON
ejpam-393	544	6	have	have	VERB
ejpam-393	544	7	us(k	us(k	ADV
ejpam-393	544	8	,	,	PUNCT
ejpam-393	544	9	l)us(k	l)us(k	ADJ
ejpam-393	544	10	,	,	PUNCT
ejpam-393	544	11	l)cucv	l)cucv	NOUN
ejpam-393	544	12	x	x	PUNCT
ejpam-393	544	13	=	=	PUNCT
ejpam-393	544	14	u	u	NOUN
ejpam-393	544	15	s(l	s(l	NOUN
ejpam-393	544	16	,	,	PUNCT
ejpam-393	544	17	k)us(k	k)us(k	ADJ
ejpam-393	544	18	,	,	PUNCT
ejpam-393	544	19	l)cucv	l)cucv	NOUN
ejpam-393	544	20	x	x	X
ejpam-393	544	21	=	=	PUNCT
ejpam-393	544	22	(	(	PUNCT
ejpam-393	544	23	by	by	ADP
ejpam-393	544	24	definition	definition	NOUN
ejpam-393	544	25	)	)	PUNCT
ejpam-393	544	26	su	su	PROPN
ejpam-393	545	1	l	l	NOUN
ejpam-393	546	1	sl	sl	INTJ
ejpam-393	547	1	k	k	INTJ
ejpam-393	547	2	sk	sk	ADP
ejpam-393	547	3	us	us	PROPN
ejpam-393	548	1	u	u	NOUN
ejpam-393	548	2	k	k	PROPN
ejpam-393	548	3	sk	sk	PROPN
ejpam-393	548	4	l	l	PROPN
ejpam-393	548	5	s	s	PART
ejpam-393	548	6	l	l	NOUN
ejpam-393	548	7	ucucv	ucucv	NOUN
ejpam-393	548	8	x	x	PUNCT
ejpam-393	548	9	=	=	PUNCT
ejpam-393	548	10	(	(	PUNCT
ejpam-393	548	11	by	by	ADP
ejpam-393	548	12	e5	e5	PROPN
ejpam-393	548	13	)	)	PUNCT
ejpam-393	548	14	su	su	PROPN
ejpam-393	549	1	l	l	NOUN
ejpam-393	550	1	sl	sl	INTJ
ejpam-393	551	1	k	k	INTJ
ejpam-393	551	2	sk	sk	ADP
ejpam-393	551	3	us	us	PROPN
ejpam-393	551	4	u	u	NOUN
ejpam-393	551	5	k	k	PROPN
ejpam-393	551	6	cks	cks	PROPN
ejpam-393	552	1	k	k	PROPN
ejpam-393	552	2	l	l	PROPN
ejpam-393	552	3	s	s	PART
ejpam-393	552	4	l	l	NOUN
ejpam-393	552	5	ucucv	ucucv	NOUN
ejpam-393	552	6	x	x	PUNCT
ejpam-393	552	7	=	=	PUNCT
ejpam-393	552	8	(	(	PUNCT
ejpam-393	552	9	by	by	ADP
ejpam-393	552	10	e8	e8	PROPN
ejpam-393	552	11	)	)	PUNCT
ejpam-393	553	1	su	su	PROPN
ejpam-393	554	1	l	l	PROPN
ejpam-393	554	2	s	s	PART
ejpam-393	554	3	l	l	X
ejpam-393	554	4	ks	ks	X
ejpam-393	554	5	u	u	PROPN
ejpam-393	554	6	ucks	uck	VERB
ejpam-393	554	7	k	k	PROPN
ejpam-393	554	8	l	l	NOUN
ejpam-393	554	9	s	s	PART
ejpam-393	554	10	l	l	NOUN
ejpam-393	554	11	ucucv	ucucv	NOUN
ejpam-393	554	12	x	x	PUNCT
ejpam-393	554	13	=	=	PUNCT
ejpam-393	554	14	(	(	PUNCT
ejpam-393	554	15	by	by	ADP
ejpam-393	554	16	e2	e2	PROPN
ejpam-393	554	17	)	)	PUNCT
ejpam-393	555	1	su	su	PROPN
ejpam-393	555	2	l	l	PROPN
ejpam-393	555	3	s	s	PART
ejpam-393	555	4	l	l	NOUN
ejpam-393	555	5	kcks	kck	NOUN
ejpam-393	555	6	k	k	PROPN
ejpam-393	555	7	l	l	PROPN
ejpam-393	555	8	s	s	PART
ejpam-393	555	9	l	l	NOUN
ejpam-393	555	10	ucucv	ucucv	NOUN
ejpam-393	555	11	x	x	PUNCT
ejpam-393	555	12	=	=	PUNCT
ejpam-393	555	13	(	(	PUNCT
ejpam-393	555	14	by	by	ADP
ejpam-393	555	15	e5	e5	PROPN
ejpam-393	555	16	)	)	PUNCT
ejpam-393	556	1	su	su	PROPN
ejpam-393	557	1	l	l	PROPN
ejpam-393	557	2	s	s	PART
ejpam-393	557	3	l	l	X
ejpam-393	557	4	ks	ks	NOUN
ejpam-393	557	5	k	k	PROPN
ejpam-393	557	6	l	l	PROPN
ejpam-393	557	7	s	s	PART
ejpam-393	557	8	l	l	NOUN
ejpam-393	557	9	ucucv	ucucv	NOUN
ejpam-393	557	10	x	x	PUNCT
ejpam-393	557	11	=	=	PUNCT
ejpam-393	557	12	(	(	PUNCT
ejpam-393	557	13	by	by	ADP
ejpam-393	557	14	e5	e5	PROPN
ejpam-393	557	15	)	)	PUNCT
ejpam-393	557	16	su	su	PROPN
ejpam-393	558	1	l	l	PROPN
ejpam-393	558	2	s	s	PART
ejpam-393	558	3	l	l	X
ejpam-393	558	4	ks	ks	NOUN
ejpam-393	558	5	k	k	PROPN
ejpam-393	558	6	l	l	PROPN
ejpam-393	558	7	cls	cls	NOUN
ejpam-393	558	8	l	l	NOUN
ejpam-393	558	9	ucucv	ucucv	NOUN
ejpam-393	558	10	x	x	PUNCT
ejpam-393	558	11	=	=	PUNCT
ejpam-393	558	12	(	(	PUNCT
ejpam-393	558	13	by	by	ADP
ejpam-393	558	14	e8	e8	PROPN
ejpam-393	558	15	)	)	PUNCT
ejpam-393	558	16	su	su	PROPN
ejpam-393	559	1	l	l	PROPN
ejpam-393	559	2	s	s	PROPN
ejpam-393	559	3	k	k	PROPN
ejpam-393	559	4	kcls	kcls	PROPN
ejpam-393	559	5	l	l	PROPN
ejpam-393	559	6	ucucv	ucucv	NOUN
ejpam-393	559	7	x	x	X
ejpam-393	559	8	=	=	PUNCT
ejpam-393	559	9	(	(	PUNCT
ejpam-393	559	10	by	by	ADP
ejpam-393	559	11	e8	e8	PROPN
ejpam-393	559	12	)	)	PUNCT
ejpam-393	559	13	su	su	PROPN
ejpam-393	560	1	l	l	PROPN
ejpam-393	560	2	s	s	PART
ejpam-393	560	3	l	l	NOUN
ejpam-393	560	4	ucucv	ucucv	NOUN
ejpam-393	560	5	x	x	PUNCT
ejpam-393	560	6	=	=	PUNCT
ejpam-393	560	7	(	(	PUNCT
ejpam-393	560	8	by	by	ADP
ejpam-393	560	9	e8	e8	PROPN
ejpam-393	560	10	)	)	PUNCT
ejpam-393	560	11	sl	sl	VERB
ejpam-393	560	12	lcucv	lcucv	NOUN
ejpam-393	560	13	x	x	NOUN
ejpam-393	560	14	=	=	PUNCT
ejpam-393	560	15	(	(	PUNCT
ejpam-393	560	16	by	by	ADP
ejpam-393	560	17	e2	e2	PROPN
ejpam-393	560	18	)	)	PUNCT
ejpam-393	560	19	cucv	cucv	PROPN
ejpam-393	560	20	x	x	X
ejpam-393	560	21	.	.	PUNCT
ejpam-393	561	1	(	(	PUNCT
ejpam-393	561	2	i	i	NOUN
ejpam-393	561	3	)	)	PUNCT
ejpam-393	561	4	and	and	CCONJ
ejpam-393	561	5	(	(	PUNCT
ejpam-393	561	6	ii	ii	NOUN
ejpam-393	561	7	)	)	PUNCT
ejpam-393	561	8	are	be	AUX
ejpam-393	561	9	sometimes	sometimes	ADV
ejpam-393	561	10	called	call	VERB
ejpam-393	561	11	the	the	DET
ejpam-393	561	12	merry	merry	ADJ
ejpam-393	561	13	-	-	PUNCT
ejpam-393	561	14	go	go	NOUN
ejpam-393	561	15	-	-	PUNCT
ejpam-393	561	16	round	round	NOUN
ejpam-393	561	17	identities	identity	NOUN
ejpam-393	561	18	[	[	X
ejpam-393	561	19	12	12	NUM
ejpam-393	561	20	]	]	PUNCT
ejpam-393	561	21	.	.	PUNCT
ejpam-393	562	1	since	since	SCONJ
ejpam-393	562	2	our	our	PRON
ejpam-393	562	3	proof	proof	NOUN
ejpam-393	562	4	is	be	AUX
ejpam-393	562	5	model	model	NOUN
ejpam-393	562	6	theoretic	theoretic	NOUN
ejpam-393	562	7	,	,	PUNCT
ejpam-393	562	8	we	we	PRON
ejpam-393	562	9	recall	recall	VERB
ejpam-393	562	10	some	some	DET
ejpam-393	562	11	notions	notion	NOUN
ejpam-393	562	12	and	and	CCONJ
ejpam-393	562	13	concepts	concept	NOUN
ejpam-393	562	14	from	from	ADP
ejpam-393	562	15	model	model	NOUN
ejpam-393	562	16	theory	theory	NOUN
ejpam-393	562	17	.	.	PUNCT
ejpam-393	563	1	a	a	DET
ejpam-393	563	2	good	good	ADJ
ejpam-393	563	3	reference	reference	NOUN
ejpam-393	563	4	is	be	AUX
ejpam-393	563	5	[	[	X
ejpam-393	563	6	6	6	NUM
ejpam-393	563	7	]	]	PUNCT
ejpam-393	563	8	.	.	PUNCT
ejpam-393	564	1	(	(	PUNCT
ejpam-393	564	2	our	our	PRON
ejpam-393	564	3	treatment	treatment	NOUN
ejpam-393	564	4	will	will	AUX
ejpam-393	564	5	be	be	AUX
ejpam-393	564	6	self	self	NOUN
ejpam-393	564	7	contained	contain	VERB
ejpam-393	564	8	.	.	PUNCT
ejpam-393	564	9	)	)	PUNCT
ejpam-393	565	1	3	3	X
ejpam-393	565	2	.	.	X
ejpam-393	566	1	some	some	DET
ejpam-393	566	2	model	model	ADJ
ejpam-393	566	3	-	-	PUNCT
ejpam-393	566	4	theoretic	theoretic	ADJ
ejpam-393	566	5	preparations	preparation	NOUN
ejpam-393	566	6	definition	definition	NOUN
ejpam-393	566	7	7	7	NUM
ejpam-393	566	8	.	.	PUNCT
ejpam-393	567	1	let	let	VERB
ejpam-393	567	2	l	l	NOUN
ejpam-393	567	3	be	be	AUX
ejpam-393	567	4	a	a	DET
ejpam-393	567	5	signature	signature	NOUN
ejpam-393	567	6	.	.	PUNCT
ejpam-393	568	1	by	by	ADP
ejpam-393	568	2	an	an	DET
ejpam-393	568	3	unnested	unnested	ADJ
ejpam-393	568	4	atomic	atomic	ADJ
ejpam-393	568	5	formula	formula	NOUN
ejpam-393	568	6	of	of	ADP
ejpam-393	568	7	signature	signature	NOUN
ejpam-393	568	8	l	l	NOUN
ejpam-393	568	9	we	we	PRON
ejpam-393	568	10	mean	mean	VERB
ejpam-393	568	11	an	an	DET
ejpam-393	568	12	atomic	atomic	ADJ
ejpam-393	568	13	formula	formula	NOUN
ejpam-393	568	14	of	of	ADP
ejpam-393	568	15	one	one	NUM
ejpam-393	568	16	of	of	ADP
ejpam-393	568	17	the	the	DET
ejpam-393	568	18	following	follow	VERB
ejpam-393	568	19	forms	form	NOUN
ejpam-393	568	20	:	:	PUNCT
ejpam-393	568	21	x	x	SYM
ejpam-393	568	22	=	=	SYM
ejpam-393	568	23	y	y	PROPN
ejpam-393	568	24	,	,	PUNCT
ejpam-393	568	25	c	c	PROPN
ejpam-393	568	26	=	=	SYM
ejpam-393	568	27	y	y	PROPN
ejpam-393	568	28	,	,	PUNCT
ejpam-393	568	29	f	f	PROPN
ejpam-393	568	30	(	(	PUNCT
ejpam-393	568	31	x̄	x̄	PROPN
ejpam-393	568	32	)	)	PUNCT
ejpam-393	568	33	=	=	SYM
ejpam-393	568	34	y	y	PROPN
ejpam-393	568	35	and	and	CCONJ
ejpam-393	568	36	r	r	PROPN
ejpam-393	568	37	(	(	PUNCT
ejpam-393	568	38	x̄	x̄	NOUN
ejpam-393	568	39	)	)	PUNCT
ejpam-393	568	40	where	where	SCONJ
ejpam-393	568	41	c	c	NOUN
ejpam-393	568	42	is	be	AUX
ejpam-393	568	43	a	a	DET
ejpam-393	568	44	constant	constant	ADJ
ejpam-393	568	45	,	,	PUNCT
ejpam-393	568	46	f	f	PROPN
ejpam-393	568	47	is	be	AUX
ejpam-393	568	48	a	a	DET
ejpam-393	568	49	function	function	NOUN
ejpam-393	568	50	symbol	symbol	NOUN
ejpam-393	568	51	and	and	CCONJ
ejpam-393	568	52	r	r	NOUN
ejpam-393	568	53	is	be	AUX
ejpam-393	568	54	a	a	DET
ejpam-393	568	55	relation	relation	NOUN
ejpam-393	568	56	symbol	symbol	NOUN
ejpam-393	568	57	.	.	PUNCT
ejpam-393	569	1	definition	definition	NOUN
ejpam-393	569	2	8	8	NUM
ejpam-393	569	3	.	.	PUNCT
ejpam-393	570	1	let	let	VERB
ejpam-393	570	2	l	l	NOUN
ejpam-393	570	3	and	and	CCONJ
ejpam-393	570	4	k	k	PROPN
ejpam-393	570	5	be	be	AUX
ejpam-393	570	6	signatures	signature	NOUN
ejpam-393	570	7	,	,	PUNCT
ejpam-393	570	8	a	a	DET
ejpam-393	570	9	a	a	DET
ejpam-393	570	10	k	k	PROPN
ejpam-393	570	11	structure	structure	NOUN
ejpam-393	570	12	b	b	PROPN
ejpam-393	570	13	an	an	DET
ejpam-393	570	14	l	l	NOUN
ejpam-393	570	15	structure	structure	NOUN
ejpam-393	570	16	and	and	CCONJ
ejpam-393	570	17	n	n	DET
ejpam-393	570	18	a	a	DET
ejpam-393	570	19	positive	positive	ADJ
ejpam-393	570	20	integer	integer	NOUN
ejpam-393	570	21	.	.	PUNCT
ejpam-393	571	1	an	an	DET
ejpam-393	571	2	n	n	CCONJ
ejpam-393	571	3	dimensional	dimensional	ADJ
ejpam-393	571	4	interpretation	interpretation	NOUN
ejpam-393	571	5	γ	γ	NOUN
ejpam-393	571	6	of	of	ADP
ejpam-393	571	7	b	b	PROPN
ejpam-393	571	8	in	in	ADP
ejpam-393	571	9	a	a	PRON
ejpam-393	571	10	is	be	AUX
ejpam-393	571	11	defined	define	VERB
ejpam-393	571	12	to	to	PART
ejpam-393	571	13	consist	consist	VERB
ejpam-393	571	14	of	of	ADP
ejpam-393	571	15	(	(	PUNCT
ejpam-393	571	16	1	1	X
ejpam-393	571	17	)	)	PUNCT
ejpam-393	571	18	a	a	DET
ejpam-393	571	19	formula	formula	NOUN
ejpam-393	571	20	∂γ(x0	∂γ(x0	PROPN
ejpam-393	571	21	,	,	PUNCT
ejpam-393	571	22	.	.	PUNCT
ejpam-393	571	23	.	.	PUNCT
ejpam-393	571	24	.	.	PUNCT
ejpam-393	572	1	xn−1	xn−1	PROPN
ejpam-393	572	2	)	)	PUNCT
ejpam-393	572	3	of	of	ADP
ejpam-393	572	4	signature	signature	NOUN
ejpam-393	572	5	k	k	PROPN
ejpam-393	572	6	,	,	PUNCT
ejpam-393	572	7	t.	t.	PROPN
ejpam-393	572	8	ahmed	ahmed	PROPN
ejpam-393	572	9	/	/	SYM
ejpam-393	572	10	eur	eur	PROPN
ejpam-393	572	11	.	.	PUNCT
ejpam-393	573	1	j.	j.	PROPN
ejpam-393	573	2	pure	pure	PROPN
ejpam-393	573	3	appl	appl	PROPN
ejpam-393	573	4	.	.	PROPN
ejpam-393	573	5	math	math	PROPN
ejpam-393	573	6	,	,	PUNCT
ejpam-393	573	7	3	3	NUM
ejpam-393	573	8	(	(	PUNCT
ejpam-393	573	9	2010	2010	NUM
ejpam-393	573	10	)	)	PUNCT
ejpam-393	573	11	,	,	PUNCT
ejpam-393	573	12	853	853	NUM
ejpam-393	573	13	-	-	SYM
ejpam-393	573	14	880	880	NUM
ejpam-393	573	15	865	865	NUM
ejpam-393	573	16	(	(	PUNCT
ejpam-393	573	17	2	2	NUM
ejpam-393	573	18	)	)	PUNCT
ejpam-393	573	19	for	for	ADP
ejpam-393	573	20	each	each	DET
ejpam-393	573	21	unnested	unnested	ADJ
ejpam-393	573	22	atomic	atomic	ADJ
ejpam-393	573	23	formula	formula	NOUN
ejpam-393	573	24	φγ	φγ	NOUN
ejpam-393	573	25	(	(	PUNCT
ejpam-393	573	26	ȳ0	ȳ0	NUM
ejpam-393	573	27	,	,	PUNCT
ejpam-393	573	28	.	.	PUNCT
ejpam-393	573	29	.	.	PUNCT
ejpam-393	573	30	.	.	PUNCT
ejpam-393	574	1	ȳm−1	ȳm−1	PROPN
ejpam-393	574	2	)	)	PUNCT
ejpam-393	575	1	a	a	DET
ejpam-393	575	2	formula	formula	NOUN
ejpam-393	575	3	φγ	φγ	VERB
ejpam-393	575	4	(	(	PUNCT
ejpam-393	575	5	x̄0	x̄0	PROPN
ejpam-393	575	6	,	,	PUNCT
ejpam-393	575	7	.	.	PUNCT
ejpam-393	575	8	.	.	PUNCT
ejpam-393	575	9	.	.	PUNCT
ejpam-393	576	1	x̄m−1	x̄m−1	PROPN
ejpam-393	576	2	)	)	PUNCT
ejpam-393	576	3	of	of	ADP
ejpam-393	576	4	signature	signature	NOUN
ejpam-393	577	1	k	k	PROPN
ejpam-393	577	2	in	in	ADP
ejpam-393	577	3	which	which	PRON
ejpam-393	577	4	the	the	DET
ejpam-393	577	5	x	x	X
ejpam-393	577	6	i	i	PRON
ejpam-393	577	7	’s	’	VERB
ejpam-393	577	8	are	be	AUX
ejpam-393	577	9	disjoint	disjoint	NOUN
ejpam-393	577	10	n	n	DET
ejpam-393	577	11	tuples	tuple	NOUN
ejpam-393	577	12	of	of	ADP
ejpam-393	577	13	distinct	distinct	ADJ
ejpam-393	577	14	variables	variable	NOUN
ejpam-393	577	15	,	,	PUNCT
ejpam-393	577	16	(	(	PUNCT
ejpam-393	577	17	3	3	X
ejpam-393	577	18	)	)	PUNCT
ejpam-393	577	19	a	a	DET
ejpam-393	577	20	surjective	surjective	ADJ
ejpam-393	577	21	map	map	NOUN
ejpam-393	577	22	fγ	fγ	ADV
ejpam-393	577	23	:	:	PUNCT
ejpam-393	577	24	∂γ	∂γ	PROPN
ejpam-393	577	25	(	(	PUNCT
ejpam-393	577	26	na)→	na)→	PROPN
ejpam-393	577	27	dom(b	dom(b	PROPN
ejpam-393	577	28	)	)	PUNCT
ejpam-393	577	29	,	,	PUNCT
ejpam-393	577	30	such	such	ADJ
ejpam-393	577	31	that	that	SCONJ
ejpam-393	577	32	for	for	ADP
ejpam-393	577	33	all	all	DET
ejpam-393	577	34	unnested	unnested	ADJ
ejpam-393	577	35	atomic	atomic	ADJ
ejpam-393	577	36	formula	formula	NOUN
ejpam-393	577	37	φ	φ	PROPN
ejpam-393	577	38	of	of	ADP
ejpam-393	577	39	l	l	PROPN
ejpam-393	577	40	and	and	CCONJ
ejpam-393	577	41	āi	āi	PROPN
ejpam-393	577	42	∈	∈	PROPN
ejpam-393	577	43	∂γ	∂γ	PROPN
ejpam-393	577	44	(	(	PUNCT
ejpam-393	577	45	na	na	NOUN
ejpam-393	577	46	)	)	PUNCT
ejpam-393	577	47	b	b	NOUN
ejpam-393	577	48	|=	|=	PUNCT
ejpam-393	577	49	φ	φ	PROPN
ejpam-393	577	50	(	(	PUNCT
ejpam-393	577	51	fγ	fγ	PROPN
ejpam-393	577	52	ā0	ā0	NOUN
ejpam-393	577	53	,	,	PUNCT
ejpam-393	577	54	.	.	PUNCT
ejpam-393	577	55	.	.	PUNCT
ejpam-393	577	56	.	.	PUNCT
ejpam-393	578	1	fγam−1)←→	fγam−1)←→	VERB
ejpam-393	578	2	a	a	DET
ejpam-393	578	3	|=	|=	NOUN
ejpam-393	578	4	φ(ā0	φ(ā0	NOUN
ejpam-393	578	5	,	,	PUNCT
ejpam-393	578	6	.	.	PUNCT
ejpam-393	578	7	.	.	PUNCT
ejpam-393	578	8	.	.	PUNCT
ejpam-393	579	1	¯am−1	¯am−1	NUM
ejpam-393	579	2	)	)	PUNCT
ejpam-393	579	3	.	.	PUNCT
ejpam-393	580	1	the	the	DET
ejpam-393	580	2	formula	formula	NOUN
ejpam-393	580	3	∂γ	∂γ	PROPN
ejpam-393	580	4	is	be	AUX
ejpam-393	580	5	the	the	DET
ejpam-393	580	6	domain	domain	NOUN
ejpam-393	580	7	formula	formula	NOUN
ejpam-393	580	8	of	of	ADP
ejpam-393	580	9	γ	γ	NOUN
ejpam-393	580	10	;	;	PUNCT
ejpam-393	580	11	the	the	DET
ejpam-393	580	12	formula	formula	NOUN
ejpam-393	580	13	∂γ	∂γ	NOUN
ejpam-393	580	14	and	and	CCONJ
ejpam-393	580	15	φt	φt	VERB
ejpam-393	580	16	for	for	ADP
ejpam-393	580	17	all	all	DET
ejpam-393	580	18	unnested	unnested	ADJ
ejpam-393	580	19	atomic	atomic	ADJ
ejpam-393	580	20	formula	formula	NOUN
ejpam-393	580	21	φ	φ	PROPN
ejpam-393	580	22	are	be	AUX
ejpam-393	580	23	the	the	DET
ejpam-393	580	24	defining	define	VERB
ejpam-393	580	25	formulas	formula	NOUN
ejpam-393	580	26	of	of	ADP
ejpam-393	580	27	γ	γ	PROPN
ejpam-393	580	28	.	.	PUNCT
ejpam-393	581	1	if	if	SCONJ
ejpam-393	581	2	γ	γ	PROPN
ejpam-393	581	3	is	be	AUX
ejpam-393	581	4	an	an	DET
ejpam-393	581	5	interpretation	interpretation	NOUN
ejpam-393	581	6	of	of	ADP
ejpam-393	581	7	an	an	DET
ejpam-393	581	8	l	l	NOUN
ejpam-393	581	9	structure	structure	NOUN
ejpam-393	581	10	b	b	PROPN
ejpam-393	581	11	in	in	ADP
ejpam-393	581	12	a	a	DET
ejpam-393	581	13	k	k	PROPN
ejpam-393	581	14	structure	structure	NOUN
ejpam-393	581	15	a	a	PRON
ejpam-393	581	16	,	,	PUNCT
ejpam-393	581	17	then	then	ADV
ejpam-393	581	18	there	there	PRON
ejpam-393	581	19	are	be	VERB
ejpam-393	581	20	certain	certain	ADJ
ejpam-393	581	21	sequences	sequence	NOUN
ejpam-393	581	22	of	of	ADP
ejpam-393	581	23	signature	signature	NOUN
ejpam-393	581	24	k	k	PROPN
ejpam-393	581	25	which	which	PRON
ejpam-393	581	26	must	must	AUX
ejpam-393	581	27	be	be	AUX
ejpam-393	581	28	true	true	ADJ
ejpam-393	581	29	in	in	ADP
ejpam-393	581	30	a	a	DET
ejpam-393	581	31	just	just	ADV
ejpam-393	581	32	becuase	becuase	ADV
ejpam-393	581	33	γ	γ	NOUN
ejpam-393	581	34	is	be	AUX
ejpam-393	581	35	an	an	DET
ejpam-393	581	36	interpretation	interpretation	NOUN
ejpam-393	581	37	,	,	PUNCT
ejpam-393	581	38	regardless	regardless	ADV
ejpam-393	581	39	of	of	ADP
ejpam-393	581	40	what	what	PRON
ejpam-393	581	41	a	a	PRON
ejpam-393	581	42	and	and	CCONJ
ejpam-393	581	43	b	b	NOUN
ejpam-393	581	44	are	be	AUX
ejpam-393	581	45	.	.	PUNCT
ejpam-393	582	1	these	these	DET
ejpam-393	582	2	sentences	sentence	NOUN
ejpam-393	582	3	say	say	VERB
ejpam-393	582	4	:	:	PUNCT
ejpam-393	582	5	(	(	PUNCT
ejpam-393	582	6	i	i	NOUN
ejpam-393	582	7	)	)	PUNCT
ejpam-393	582	8	let	let	VERB
ejpam-393	582	9	=	=	PRON
ejpam-393	582	10	γ	γ	X
ejpam-393	582	11	be	be	AUX
ejpam-393	582	12	φγ	φγ	VERB
ejpam-393	582	13	when	when	SCONJ
ejpam-393	582	14	φ	φ	PROPN
ejpam-393	582	15	is	be	AUX
ejpam-393	582	16	y0	y0	PROPN
ejpam-393	582	17	=	=	SYM
ejpam-393	582	18	y1	y1	PROPN
ejpam-393	582	19	.	.	PUNCT
ejpam-393	583	1	then	then	ADV
ejpam-393	583	2	=	=	NOUN
ejpam-393	583	3	γ	γ	X
ejpam-393	583	4	is	be	AUX
ejpam-393	583	5	an	an	DET
ejpam-393	583	6	equivalence	equivalence	NOUN
ejpam-393	583	7	relation	relation	NOUN
ejpam-393	583	8	.	.	PUNCT
ejpam-393	584	1	(	(	PUNCT
ejpam-393	584	2	ii	ii	NOUN
ejpam-393	584	3	)	)	PUNCT
ejpam-393	584	4	for	for	ADP
ejpam-393	584	5	each	each	DET
ejpam-393	584	6	unnested	unnested	ADJ
ejpam-393	584	7	atomic	atomic	ADJ
ejpam-393	584	8	formula	formula	NOUN
ejpam-393	584	9	φ	φ	PROPN
ejpam-393	584	10	of	of	ADP
ejpam-393	584	11	l	l	PROPN
ejpam-393	584	12	,	,	PUNCT
ejpam-393	584	13	if	if	SCONJ
ejpam-393	584	14	a	a	DET
ejpam-393	584	15	|=	|=	NOUN
ejpam-393	584	16	φγ(ā0	φγ(ā0	ADP
ejpam-393	584	17	,	,	PUNCT
ejpam-393	584	18	.	.	PUNCT
ejpam-393	584	19	.	.	PUNCT
ejpam-393	584	20	.	.	PUNCT
ejpam-393	585	1	¯an−1	¯an−1	NUM
ejpam-393	585	2	)	)	PUNCT
ejpam-393	585	3	where	where	SCONJ
ejpam-393	585	4	ā0	ā0	ADV
ejpam-393	585	5	,	,	PUNCT
ejpam-393	585	6	.	.	PUNCT
ejpam-393	585	7	.	.	PUNCT
ejpam-393	585	8	.	.	PUNCT
ejpam-393	586	1	¯an−1	¯an−1	X
ejpam-393	586	2	∈	∈	PROPN
ejpam-393	586	3	∂	∂	NUM
ejpam-393	586	4	n	n	ADP
ejpam-393	586	5	γ	γ	X
ejpam-393	586	6	a	a	X
ejpam-393	586	7	,	,	PUNCT
ejpam-393	586	8	then	then	ADV
ejpam-393	586	9	also	also	ADV
ejpam-393	586	10	a	a	DET
ejpam-393	586	11	|=	|=	NOUN
ejpam-393	586	12	φγ	φγ	NOUN
ejpam-393	586	13	(	(	PUNCT
ejpam-393	586	14	b̄0	b̄0	NOUN
ejpam-393	586	15	.	.	PUNCT
ejpam-393	586	16	.	.	PUNCT
ejpam-393	586	17	.	.	PUNCT
ejpam-393	587	1	¯bn−1	¯bn−1	PROPN
ejpam-393	587	2	)	)	PUNCT
ejpam-393	587	3	where	where	SCONJ
ejpam-393	587	4	each	each	DET
ejpam-393	587	5	b̄i	b̄i	PROPN
ejpam-393	587	6	is	be	AUX
ejpam-393	587	7	an	an	DET
ejpam-393	587	8	element	element	NOUN
ejpam-393	587	9	of	of	ADP
ejpam-393	587	10	∂γ	∂γ	PROPN
ejpam-393	587	11	(	(	PUNCT
ejpam-393	587	12	na	na	NOUN
ejpam-393	587	13	)	)	PUNCT
ejpam-393	587	14	which	which	PRON
ejpam-393	587	15	is	be	AUX
ejpam-393	587	16	=	=	PRON
ejpam-393	587	17	γ	γ	X
ejpam-393	587	18	equivalent	equivalent	ADJ
ejpam-393	587	19	to	to	ADP
ejpam-393	587	20	āi	āi	PROPN
ejpam-393	587	21	.	.	PUNCT
ejpam-393	588	1	(	(	PUNCT
ejpam-393	588	2	iii	iii	X
ejpam-393	588	3	)	)	PUNCT
ejpam-393	588	4	if	if	SCONJ
ejpam-393	588	5	φ(y0	φ(y0	NOUN
ejpam-393	588	6	)	)	PUNCT
ejpam-393	588	7	is	be	AUX
ejpam-393	588	8	a	a	DET
ejpam-393	588	9	formula	formula	NOUN
ejpam-393	588	10	of	of	ADP
ejpam-393	588	11	l	l	NOUN
ejpam-393	588	12	of	of	ADP
ejpam-393	588	13	the	the	DET
ejpam-393	588	14	form	form	NOUN
ejpam-393	588	15	c	c	NOUN
ejpam-393	588	16	=	=	SYM
ejpam-393	588	17	y0	y0	NOUN
ejpam-393	588	18	,	,	PUNCT
ejpam-393	588	19	then	then	ADV
ejpam-393	588	20	there	there	PRON
ejpam-393	588	21	is	be	VERB
ejpam-393	588	22	an	an	DET
ejpam-393	588	23	ā	ā	NOUN
ejpam-393	588	24	in	in	ADP
ejpam-393	588	25	∂γ	∂γ	PROPN
ejpam-393	588	26	(	(	PUNCT
ejpam-393	588	27	na)such	na)such	ADV
ejpam-393	588	28	that	that	SCONJ
ejpam-393	588	29	for	for	ADP
ejpam-393	588	30	all	all	DET
ejpam-393	588	31	b̄	b̄	NOUN
ejpam-393	588	32	in	in	ADP
ejpam-393	588	33	∂γ	∂γ	PROPN
ejpam-393	588	34	(	(	PUNCT
ejpam-393	588	35	na	na	NOUN
ejpam-393	588	36	)	)	PUNCT
ejpam-393	588	37	,	,	PUNCT
ejpam-393	588	38	a	a	DET
ejpam-393	588	39	|=	|=	NOUN
ejpam-393	588	40	φγ	φγ	ADP
ejpam-393	588	41	b̄	b̄	NOUN
ejpam-393	588	42	if	if	SCONJ
ejpam-393	588	43	b̄	b̄	PROPN
ejpam-393	588	44	is	be	AUX
ejpam-393	588	45	=	=	NOUN
ejpam-393	588	46	γ	γ	X
ejpam-393	588	47	equivalent	equivalent	ADJ
ejpam-393	588	48	to	to	ADP
ejpam-393	588	49	ā.	ā.	PROPN
ejpam-393	588	50	(	(	PUNCT
ejpam-393	588	51	iv	iv	X
ejpam-393	588	52	)	)	PUNCT
ejpam-393	588	53	a	a	DET
ejpam-393	588	54	clause	clause	NOUN
ejpam-393	588	55	like	like	ADP
ejpam-393	588	56	(	(	PUNCT
ejpam-393	588	57	iii	iii	NOUN
ejpam-393	588	58	)	)	PUNCT
ejpam-393	588	59	for	for	ADP
ejpam-393	588	60	each	each	DET
ejpam-393	588	61	function	function	NOUN
ejpam-393	588	62	symbol	symbol	NOUN
ejpam-393	588	63	.	.	PUNCT
ejpam-393	589	1	for	for	ADP
ejpam-393	589	2	a	a	DET
ejpam-393	589	3	signature	signature	NOUN
ejpam-393	589	4	l	l	NOUN
ejpam-393	589	5	,	,	PUNCT
ejpam-393	589	6	l∞ω	l∞ω	PROPN
ejpam-393	589	7	denotes	denote	VERB
ejpam-393	589	8	the	the	DET
ejpam-393	589	9	extension	extension	NOUN
ejpam-393	589	10	of	of	ADP
ejpam-393	589	11	the	the	DET
ejpam-393	589	12	first	first	ADJ
ejpam-393	589	13	order	order	NOUN
ejpam-393	589	14	language	language	NOUN
ejpam-393	589	15	of	of	ADP
ejpam-393	589	16	l	l	NOUN
ejpam-393	589	17	by	by	ADP
ejpam-393	589	18	infinitary	infinitary	ADJ
ejpam-393	589	19	conjunctions	conjunction	NOUN
ejpam-393	589	20	and	and	CCONJ
ejpam-393	589	21	disjunctions	disjunction	NOUN
ejpam-393	589	22	.	.	PUNCT
ejpam-393	590	1	the	the	DET
ejpam-393	590	2	following	follow	VERB
ejpam-393	590	3	lemma	lemma	PROPN
ejpam-393	590	4	is	be	AUX
ejpam-393	590	5	more	more	ADV
ejpam-393	590	6	general	general	ADJ
ejpam-393	590	7	than	than	ADP
ejpam-393	590	8	what	what	PRON
ejpam-393	590	9	we	we	PRON
ejpam-393	590	10	need	need	VERB
ejpam-393	590	11	(	(	PUNCT
ejpam-393	590	12	however	however	ADV
ejpam-393	590	13	the	the	DET
ejpam-393	590	14	proof	proof	NOUN
ejpam-393	590	15	is	be	AUX
ejpam-393	590	16	the	the	DET
ejpam-393	590	17	same	same	ADJ
ejpam-393	590	18	):	):	PUNCT
ejpam-393	590	19	lemma	lemma	PROPN
ejpam-393	590	20	5	5	NUM
ejpam-393	590	21	.	.	PUNCT
ejpam-393	591	1	let	let	VERB
ejpam-393	591	2	a	a	DET
ejpam-393	591	3	be	be	AUX
ejpam-393	591	4	a	a	DET
ejpam-393	591	5	k	k	NOUN
ejpam-393	591	6	structure	structure	NOUN
ejpam-393	591	7	,	,	PUNCT
ejpam-393	591	8	b	b	PROPN
ejpam-393	591	9	an	an	DET
ejpam-393	591	10	l	l	NOUN
ejpam-393	591	11	structure	structure	NOUN
ejpam-393	591	12	and	and	CCONJ
ejpam-393	591	13	γ	γ	X
ejpam-393	591	14	an	an	DET
ejpam-393	591	15	n	n	NUM
ejpam-393	591	16	interpretation	interpretation	NOUN
ejpam-393	591	17	of	of	ADP
ejpam-393	591	18	b	b	PROPN
ejpam-393	591	19	in	in	ADP
ejpam-393	591	20	a.	a.	NOUN
ejpam-393	591	21	then	then	ADV
ejpam-393	591	22	for	for	ADP
ejpam-393	591	23	every	every	DET
ejpam-393	591	24	formula	formula	NOUN
ejpam-393	591	25	φ	φ	X
ejpam-393	591	26	(	(	PUNCT
ejpam-393	591	27	ȳ	ȳ	PROPN
ejpam-393	591	28	)	)	PUNCT
ejpam-393	591	29	of	of	ADP
ejpam-393	591	30	the	the	DET
ejpam-393	591	31	language	language	NOUN
ejpam-393	591	32	l∞ω	l∞ω	NOUN
ejpam-393	591	33	there	there	PRON
ejpam-393	591	34	is	be	VERB
ejpam-393	591	35	a	a	DET
ejpam-393	591	36	formula	formula	NOUN
ejpam-393	591	37	φγ(x	φγ(x	NOUN
ejpam-393	591	38	)	)	PUNCT
ejpam-393	591	39	of	of	ADP
ejpam-393	591	40	the	the	DET
ejpam-393	591	41	language	language	NOUN
ejpam-393	591	42	k∞ω	k∞ω	NOUN
ejpam-393	591	43	such	such	ADJ
ejpam-393	591	44	that	that	SCONJ
ejpam-393	591	45	b	b	X
ejpam-393	591	46	|=	|=	PUNCT
ejpam-393	591	47	φ	φ	X
ejpam-393	591	48	(	(	PUNCT
ejpam-393	591	49	fγ	fγ	PROPN
ejpam-393	591	50	ā)←→	ā)←→	PROPN
ejpam-393	591	51	a	a	DET
ejpam-393	591	52	|=	|=	NOUN
ejpam-393	591	53	φγ(ā	φγ(ā	NOUN
ejpam-393	591	54	)	)	PUNCT
ejpam-393	591	55	proof	proof	NOUN
ejpam-393	591	56	.	.	PUNCT
ejpam-393	592	1	every	every	DET
ejpam-393	592	2	formula	formula	NOUN
ejpam-393	592	3	of	of	ADP
ejpam-393	592	4	l∞ω	l∞ω	NOUN
ejpam-393	592	5	is	be	AUX
ejpam-393	592	6	equivalent	equivalent	ADJ
ejpam-393	592	7	to	to	ADP
ejpam-393	592	8	a	a	DET
ejpam-393	592	9	formula	formula	NOUN
ejpam-393	592	10	in	in	ADP
ejpam-393	592	11	which	which	PRON
ejpam-393	592	12	all	all	DET
ejpam-393	592	13	atomic	atomic	ADJ
ejpam-393	592	14	subformulas	subformula	NOUN
ejpam-393	592	15	are	be	AUX
ejpam-393	592	16	nested	nest	VERB
ejpam-393	592	17	.	.	PUNCT
ejpam-393	593	1	we	we	PRON
ejpam-393	593	2	prove	prove	VERB
ejpam-393	593	3	the	the	DET
ejpam-393	593	4	theorem	theorem	NOUN
ejpam-393	593	5	by	by	ADP
ejpam-393	593	6	induction	induction	NOUN
ejpam-393	593	7	on	on	ADP
ejpam-393	593	8	complexity	complexity	NOUN
ejpam-393	593	9	of	of	ADP
ejpam-393	593	10	formulas	formula	NOUN
ejpam-393	593	11	,	,	PUNCT
ejpam-393	593	12	and	and	CCONJ
ejpam-393	593	13	definition	definition	NOUN
ejpam-393	593	14	6	6	NUM
ejpam-393	593	15	takes	take	VERB
ejpam-393	593	16	care	care	NOUN
ejpam-393	593	17	for	for	ADP
ejpam-393	593	18	the	the	DET
ejpam-393	593	19	atomic	atomic	ADJ
ejpam-393	593	20	formulas	formula	NOUN
ejpam-393	593	21	.	.	PUNCT
ejpam-393	594	1	for	for	ADP
ejpam-393	594	2	compound	compound	NOUN
ejpam-393	594	3	formulas	formula	NOUN
ejpam-393	594	4	,	,	PUNCT
ejpam-393	594	5	we	we	PRON
ejpam-393	594	6	define	define	VERB
ejpam-393	594	7	:	:	PUNCT
ejpam-393	594	8	(	(	PUNCT
ejpam-393	594	9	¬φ)γ	¬φ)γ	X
ejpam-393	594	10	=	=	SYM
ejpam-393	594	11	¬(φγ	¬(φγ	NUM
ejpam-393	594	12	)	)	PUNCT
ejpam-393	594	13	,	,	PUNCT
ejpam-393	594	14	(	(	PUNCT
ejpam-393	594	15	∧	∧	PROPN
ejpam-393	594	16	φi)γ	φi)γ	PROPN
ejpam-393	594	17	=	=	SYM
ejpam-393	594	18	∧	∧	PROPN
ejpam-393	594	19	(	(	PUNCT
ejpam-393	594	20	φi)γ	φi)γ	NOUN
ejpam-393	594	21	and	and	CCONJ
ejpam-393	594	22	likewise	likewise	ADV
ejpam-393	594	23	with	with	ADP
ejpam-393	594	24	∨	∨	NUM
ejpam-393	594	25	(	(	PUNCT
ejpam-393	594	26	∃yφ)γ	∃yφ)γ	PROPN
ejpam-393	594	27	=	=	SYM
ejpam-393	594	28	∃x0	∃x0	PROPN
ejpam-393	594	29	.	.	PUNCT
ejpam-393	594	30	.	.	PUNCT
ejpam-393	594	31	.	.	PUNCT
ejpam-393	595	1	xn−1(∂γ(x0	xn−1(∂γ(x0	X
ejpam-393	595	2	,	,	PUNCT
ejpam-393	595	3	.	.	PUNCT
ejpam-393	595	4	.	.	PUNCT
ejpam-393	595	5	.	.	PUNCT
ejpam-393	596	1	,	,	PUNCT
ejpam-393	596	2	xn−1)∧φγ	xn−1)∧φγ	PROPN
ejpam-393	596	3	)	)	PUNCT
ejpam-393	596	4	.	.	PUNCT
ejpam-393	597	1	we	we	PRON
ejpam-393	597	2	need	need	VERB
ejpam-393	597	3	to	to	PART
ejpam-393	597	4	show	show	VERB
ejpam-393	597	5	that	that	SCONJ
ejpam-393	597	6	elementary	elementary	ADJ
ejpam-393	597	7	equivalence	equivalence	NOUN
ejpam-393	597	8	is	be	AUX
ejpam-393	597	9	preserved	preserve	VERB
ejpam-393	597	10	by	by	ADP
ejpam-393	597	11	taking	take	VERB
ejpam-393	597	12	products	product	NOUN
ejpam-393	597	13	.	.	PUNCT
ejpam-393	598	1	for	for	ADP
ejpam-393	598	2	this	this	DET
ejpam-393	598	3	purpose	purpose	NOUN
ejpam-393	598	4	we	we	PRON
ejpam-393	598	5	devise	devise	VERB
ejpam-393	598	6	a	a	DET
ejpam-393	598	7	game	game	NOUN
ejpam-393	598	8	between	between	ADP
ejpam-393	598	9	∀	∀	X
ejpam-393	598	10	(	(	PUNCT
ejpam-393	598	11	male	male	NOUN
ejpam-393	598	12	)	)	PUNCT
ejpam-393	598	13	and	and	CCONJ
ejpam-393	598	14	∃(female	∃(female	NUM
ejpam-393	598	15	)	)	PUNCT
ejpam-393	598	16	.	.	PUNCT
ejpam-393	599	1	we	we	PRON
ejpam-393	599	2	imagine	imagine	VERB
ejpam-393	599	3	that	that	SCONJ
ejpam-393	599	4	∀wants	∀want	NOUN
ejpam-393	599	5	to	to	PART
ejpam-393	599	6	prove	prove	VERB
ejpam-393	599	7	that	that	SCONJ
ejpam-393	599	8	a	a	PRON
ejpam-393	599	9	is	be	AUX
ejpam-393	599	10	different	different	ADJ
ejpam-393	599	11	from	from	ADP
ejpam-393	599	12	b	b	NOUN
ejpam-393	599	13	while	while	SCONJ
ejpam-393	599	14	∃	∃	PROPN
ejpam-393	599	15	tries	try	VERB
ejpam-393	599	16	to	to	PART
ejpam-393	599	17	show	show	VERB
ejpam-393	599	18	that	that	SCONJ
ejpam-393	599	19	a	a	PRON
ejpam-393	599	20	is	be	AUX
ejpam-393	599	21	the	the	DET
ejpam-393	599	22	same	same	ADJ
ejpam-393	599	23	as	as	ADP
ejpam-393	599	24	b.	b.	PROPN
ejpam-393	600	1	so	so	ADV
ejpam-393	600	2	their	their	PRON
ejpam-393	600	3	conversation	conversation	NOUN
ejpam-393	600	4	has	have	VERB
ejpam-393	600	5	the	the	DET
ejpam-393	600	6	form	form	NOUN
ejpam-393	600	7	of	of	ADP
ejpam-393	600	8	a	a	DET
ejpam-393	600	9	game	game	NOUN
ejpam-393	600	10	.	.	PUNCT
ejpam-393	601	1	player	player	NOUN
ejpam-393	601	2	∀	∀	NOUN
ejpam-393	601	3	wins	win	VERB
ejpam-393	601	4	if	if	SCONJ
ejpam-393	601	5	he	he	PRON
ejpam-393	601	6	manages	manage	VERB
ejpam-393	601	7	to	to	PART
ejpam-393	601	8	find	find	VERB
ejpam-393	601	9	a	a	DET
ejpam-393	601	10	difference	difference	NOUN
ejpam-393	601	11	between	between	ADP
ejpam-393	601	12	a	a	PRON
ejpam-393	601	13	and	and	CCONJ
ejpam-393	601	14	b	b	NOUN
ejpam-393	601	15	t.	t.	PROPN
ejpam-393	601	16	ahmed	ahmed	PROPN
ejpam-393	601	17	/	/	SYM
ejpam-393	601	18	eur	eur	PROPN
ejpam-393	601	19	.	.	PUNCT
ejpam-393	602	1	j.	j.	PROPN
ejpam-393	602	2	pure	pure	PROPN
ejpam-393	602	3	appl	appl	PROPN
ejpam-393	602	4	.	.	PROPN
ejpam-393	602	5	math	math	PROPN
ejpam-393	602	6	,	,	PUNCT
ejpam-393	602	7	3	3	NUM
ejpam-393	602	8	(	(	PUNCT
ejpam-393	602	9	2010	2010	NUM
ejpam-393	602	10	)	)	PUNCT
ejpam-393	602	11	,	,	PUNCT
ejpam-393	602	12	853	853	NUM
ejpam-393	602	13	-	-	SYM
ejpam-393	602	14	880	880	NUM
ejpam-393	602	15	866	866	NUM
ejpam-393	602	16	before	before	SCONJ
ejpam-393	602	17	the	the	DET
ejpam-393	602	18	play	play	NOUN
ejpam-393	602	19	is	be	AUX
ejpam-393	602	20	over	over	ADV
ejpam-393	602	21	;	;	PUNCT
ejpam-393	602	22	otherwise	otherwise	ADV
ejpam-393	602	23	∃	∃	PROPN
ejpam-393	602	24	wins	win	VERB
ejpam-393	602	25	.	.	PUNCT
ejpam-393	603	1	the	the	DET
ejpam-393	603	2	game	game	NOUN
ejpam-393	603	3	is	be	AUX
ejpam-393	603	4	played	play	VERB
ejpam-393	603	5	in	in	ADP
ejpam-393	603	6	µ≤ω	µ≤ω	PROPN
ejpam-393	603	7	steps	step	NOUN
ejpam-393	603	8	.	.	PUNCT
ejpam-393	604	1	at	at	ADP
ejpam-393	604	2	the	the	DET
ejpam-393	604	3	ith	ith	PROPN
ejpam-393	604	4	step	step	NOUN
ejpam-393	604	5	of	of	ADP
ejpam-393	604	6	a	a	DET
ejpam-393	604	7	play	play	NOUN
ejpam-393	604	8	,	,	PUNCT
ejpam-393	604	9	player	player	NOUN
ejpam-393	604	10	∀	∀	NOUN
ejpam-393	604	11	takes	take	VERB
ejpam-393	604	12	one	one	NUM
ejpam-393	604	13	of	of	ADP
ejpam-393	604	14	the	the	DET
ejpam-393	604	15	structures	structure	NOUN
ejpam-393	604	16	a	a	DET
ejpam-393	604	17	,	,	PUNCT
ejpam-393	604	18	b	b	NOUN
ejpam-393	604	19	and	and	CCONJ
ejpam-393	604	20	chooses	choose	VERB
ejpam-393	604	21	an	an	DET
ejpam-393	604	22	element	element	NOUN
ejpam-393	604	23	this	this	DET
ejpam-393	604	24	structure	structure	NOUN
ejpam-393	604	25	;	;	PUNCT
ejpam-393	604	26	then	then	ADV
ejpam-393	604	27	∃	∃	PROPN
ejpam-393	604	28	chooses	choose	VERB
ejpam-393	604	29	an	an	DET
ejpam-393	604	30	atom	atom	NOUN
ejpam-393	604	31	of	of	ADP
ejpam-393	604	32	the	the	DET
ejpam-393	604	33	other	other	ADJ
ejpam-393	604	34	structure	structure	NOUN
ejpam-393	604	35	.	.	PUNCT
ejpam-393	605	1	so	so	ADV
ejpam-393	605	2	between	between	ADP
ejpam-393	605	3	them	they	PRON
ejpam-393	605	4	they	they	PRON
ejpam-393	605	5	choose	choose	VERB
ejpam-393	605	6	an	an	DET
ejpam-393	605	7	element	element	NOUN
ejpam-393	605	8	ai	ai	NOUN
ejpam-393	605	9	of	of	ADP
ejpam-393	605	10	a	a	PRON
ejpam-393	605	11	and	and	CCONJ
ejpam-393	605	12	an	an	DET
ejpam-393	605	13	element	element	ADJ
ejpam-393	605	14	bi	bi	NOUN
ejpam-393	605	15	of	of	ADP
ejpam-393	605	16	b.	b.	PROPN
ejpam-393	606	1	apart	apart	ADV
ejpam-393	606	2	from	from	ADP
ejpam-393	606	3	the	the	DET
ejpam-393	606	4	fact	fact	NOUN
ejpam-393	606	5	that	that	SCONJ
ejpam-393	606	6	player	player	NOUN
ejpam-393	606	7	∃	∃	PROPN
ejpam-393	606	8	must	must	AUX
ejpam-393	606	9	choose	choose	VERB
ejpam-393	606	10	from	from	ADP
ejpam-393	606	11	the	the	DET
ejpam-393	606	12	other	other	ADJ
ejpam-393	606	13	structure	structure	NOUN
ejpam-393	606	14	from	from	ADP
ejpam-393	606	15	player	player	NOUN
ejpam-393	606	16	∀	∀	NOUN
ejpam-393	606	17	at	at	ADP
ejpam-393	606	18	each	each	DET
ejpam-393	606	19	step	step	NOUN
ejpam-393	606	20	,	,	PUNCT
ejpam-393	606	21	both	both	DET
ejpam-393	606	22	players	player	NOUN
ejpam-393	606	23	have	have	VERB
ejpam-393	606	24	complete	complete	ADJ
ejpam-393	606	25	freedom	freedom	NOUN
ejpam-393	606	26	to	to	PART
ejpam-393	606	27	choose	choose	VERB
ejpam-393	606	28	as	as	SCONJ
ejpam-393	606	29	they	they	PRON
ejpam-393	606	30	please	please	VERB
ejpam-393	606	31	;	;	PUNCT
ejpam-393	606	32	in	in	ADP
ejpam-393	606	33	particular	particular	ADJ
ejpam-393	606	34	,	,	PUNCT
ejpam-393	606	35	either	either	CCONJ
ejpam-393	606	36	player	player	NOUN
ejpam-393	606	37	can	can	AUX
ejpam-393	606	38	choose	choose	VERB
ejpam-393	606	39	an	an	DET
ejpam-393	606	40	element	element	NOUN
ejpam-393	606	41	which	which	PRON
ejpam-393	606	42	was	be	AUX
ejpam-393	606	43	chosen	choose	VERB
ejpam-393	606	44	at	at	ADP
ejpam-393	606	45	an	an	DET
ejpam-393	606	46	earlier	early	ADJ
ejpam-393	606	47	step	step	NOUN
ejpam-393	606	48	.	.	PUNCT
ejpam-393	607	1	player	player	NOUN
ejpam-393	607	2	∃	∃	PROPN
ejpam-393	607	3	is	be	AUX
ejpam-393	607	4	allowed	allow	VERB
ejpam-393	607	5	to	to	PART
ejpam-393	607	6	see	see	VERB
ejpam-393	607	7	and	and	CCONJ
ejpam-393	607	8	remember	remember	VERB
ejpam-393	607	9	all	all	DET
ejpam-393	607	10	previous	previous	ADJ
ejpam-393	607	11	moves	move	NOUN
ejpam-393	607	12	in	in	ADP
ejpam-393	607	13	the	the	DET
ejpam-393	607	14	play	play	NOUN
ejpam-393	607	15	.	.	PUNCT
ejpam-393	608	1	(	(	PUNCT
ejpam-393	608	2	as	as	SCONJ
ejpam-393	608	3	the	the	DET
ejpam-393	608	4	game	game	NOUN
ejpam-393	608	5	theorists	theorist	NOUN
ejpam-393	608	6	would	would	AUX
ejpam-393	608	7	say	say	VERB
ejpam-393	608	8	,	,	PUNCT
ejpam-393	608	9	this	this	PRON
ejpam-393	608	10	is	be	AUX
ejpam-393	608	11	a	a	DET
ejpam-393	608	12	game	game	NOUN
ejpam-393	608	13	of	of	ADP
ejpam-393	608	14	perfect	perfect	ADJ
ejpam-393	608	15	information	information	NOUN
ejpam-393	608	16	.	.	PUNCT
ejpam-393	608	17	)	)	PUNCT
ejpam-393	609	1	at	at	ADP
ejpam-393	609	2	the	the	DET
ejpam-393	609	3	end	end	NOUN
ejpam-393	609	4	of	of	ADP
ejpam-393	609	5	the	the	DET
ejpam-393	609	6	play	play	NOUN
ejpam-393	609	7	sequences	sequence	NOUN
ejpam-393	609	8	ā	ā	NOUN
ejpam-393	609	9	=	=	PUNCT
ejpam-393	609	10	(	(	PUNCT
ejpam-393	609	11	ai	ai	INTJ
ejpam-393	609	12	:	:	PUNCT
ejpam-393	609	13	i	i	PRON
ejpam-393	609	14	<	<	X
ejpam-393	609	15	µ	µ	X
ejpam-393	609	16	)	)	PUNCT
ejpam-393	609	17	and	and	CCONJ
ejpam-393	609	18	b̄	b̄	VERB
ejpam-393	609	19	=	=	PUNCT
ejpam-393	609	20	(	(	PUNCT
ejpam-393	609	21	bi	bi	NOUN
ejpam-393	609	22	:	:	PUNCT
ejpam-393	609	23	i	i	PRON
ejpam-393	609	24	<	<	X
ejpam-393	609	25	µ	µ	X
ejpam-393	609	26	)	)	PUNCT
ejpam-393	609	27	have	have	AUX
ejpam-393	609	28	been	be	AUX
ejpam-393	609	29	chosen	choose	VERB
ejpam-393	609	30	.	.	PUNCT
ejpam-393	610	1	the	the	DET
ejpam-393	610	2	pair	pair	NOUN
ejpam-393	610	3	(	(	PUNCT
ejpam-393	610	4	ā	ā	NOUN
ejpam-393	610	5	,	,	PUNCT
ejpam-393	610	6	b̄	b̄	PROPN
ejpam-393	610	7	)	)	PUNCT
ejpam-393	610	8	is	be	AUX
ejpam-393	610	9	known	know	VERB
ejpam-393	610	10	as	as	ADP
ejpam-393	610	11	the	the	DET
ejpam-393	610	12	play	play	NOUN
ejpam-393	610	13	.	.	PUNCT
ejpam-393	611	1	we	we	PRON
ejpam-393	611	2	count	count	VERB
ejpam-393	611	3	the	the	DET
ejpam-393	611	4	play	play	NOUN
ejpam-393	611	5	(	(	PUNCT
ejpam-393	611	6	ā	ā	NOUN
ejpam-393	611	7	,	,	PUNCT
ejpam-393	611	8	b̄	b̄	PROPN
ejpam-393	611	9	)	)	PUNCT
ejpam-393	611	10	as	as	ADP
ejpam-393	611	11	a	a	DET
ejpam-393	611	12	win	win	NOUN
ejpam-393	611	13	for	for	ADP
ejpam-393	611	14	player	player	NOUN
ejpam-393	611	15	∃	∃	PROPN
ejpam-393	611	16	,	,	PUNCT
ejpam-393	611	17	and	and	CCONJ
ejpam-393	611	18	we	we	PRON
ejpam-393	611	19	say	say	VERB
ejpam-393	611	20	that	that	SCONJ
ejpam-393	611	21	∃	∃	PROPN
ejpam-393	611	22	wins	win	VERB
ejpam-393	611	23	the	the	DET
ejpam-393	611	24	play	play	NOUN
ejpam-393	611	25	,	,	PUNCT
ejpam-393	611	26	if	if	SCONJ
ejpam-393	611	27	for	for	ADP
ejpam-393	611	28	every	every	DET
ejpam-393	611	29	unnested	unnested	ADJ
ejpam-393	611	30	atomic	atomic	ADJ
ejpam-393	611	31	formula	formula	NOUN
ejpam-393	611	32	φ	φ	PROPN
ejpam-393	611	33	of	of	ADP
ejpam-393	611	34	l	l	NOUN
ejpam-393	611	35	a	a	DET
ejpam-393	611	36	|=	|=	NOUN
ejpam-393	611	37	φ(ā)←→b	φ(ā)←→b	ADJ
ejpam-393	611	38	|=	|=	X
ejpam-393	611	39	φ	φ	X
ejpam-393	611	40	(	(	PUNCT
ejpam-393	611	41	b̄	b̄	PROPN
ejpam-393	611	42	)	)	PUNCT
ejpam-393	611	43	let	let	VERB
ejpam-393	611	44	us	we	PRON
ejpam-393	611	45	denote	denote	VERB
ejpam-393	611	46	this	this	DET
ejpam-393	611	47	game	game	NOUN
ejpam-393	611	48	by	by	ADP
ejpam-393	611	49	efµ(a	efµ(a	PROPN
ejpam-393	611	50	,	,	PUNCT
ejpam-393	611	51	b	b	NOUN
ejpam-393	611	52	)	)	PUNCT
ejpam-393	611	53	.	.	PUNCT
ejpam-393	612	1	(	(	PUNCT
ejpam-393	612	2	it	it	PRON
ejpam-393	612	3	is	be	AUX
ejpam-393	612	4	an	an	DET
ejpam-393	612	5	instance	instance	NOUN
ejpam-393	612	6	of	of	ADP
ejpam-393	612	7	an	an	DET
ejpam-393	612	8	ehrenfeuch	ehrenfeuch	ADJ
ejpam-393	612	9	-	-	PUNCT
ejpam-393	612	10	fraisse	fraisse	NOUN
ejpam-393	612	11	game	game	NOUN
ejpam-393	612	12	.	.	PUNCT
ejpam-393	612	13	)	)	PUNCT
ejpam-393	613	1	the	the	PRON
ejpam-393	613	2	more	more	ADV
ejpam-393	613	3	a	a	PRON
ejpam-393	613	4	is	be	AUX
ejpam-393	613	5	like	like	ADP
ejpam-393	613	6	b	b	NOUN
ejpam-393	613	7	,	,	PUNCT
ejpam-393	613	8	the	the	DET
ejpam-393	613	9	better	well	ADJ
ejpam-393	613	10	chance	chance	NOUN
ejpam-393	613	11	player	player	NOUN
ejpam-393	613	12	∃	∃	PROPN
ejpam-393	613	13	has	have	VERB
ejpam-393	613	14	of	of	ADP
ejpam-393	613	15	winning	win	VERB
ejpam-393	613	16	these	these	DET
ejpam-393	613	17	games	game	NOUN
ejpam-393	613	18	.	.	PUNCT
ejpam-393	614	1	for	for	ADP
ejpam-393	614	2	example	example	NOUN
ejpam-393	614	3	if	if	SCONJ
ejpam-393	614	4	player	player	PROPN
ejpam-393	614	5	∃	∃	PROPN
ejpam-393	614	6	knows	know	VERB
ejpam-393	614	7	about	about	ADP
ejpam-393	614	8	an	an	DET
ejpam-393	614	9	isomorphism	isomorphism	NOUN
ejpam-393	614	10	i	i	PRON
ejpam-393	614	11	:	:	PUNCT
ejpam-393	614	12	a→b	a→b	NUM
ejpam-393	614	13	then	then	ADV
ejpam-393	614	14	she	she	PRON
ejpam-393	614	15	can	can	AUX
ejpam-393	614	16	be	be	AUX
ejpam-393	614	17	sure	sure	ADJ
ejpam-393	614	18	of	of	ADP
ejpam-393	614	19	winning	win	VERB
ejpam-393	614	20	every	every	DET
ejpam-393	614	21	time	time	NOUN
ejpam-393	614	22	.	.	PUNCT
ejpam-393	615	1	all	all	PRON
ejpam-393	615	2	she	she	PRON
ejpam-393	615	3	has	have	VERB
ejpam-393	615	4	to	to	PART
ejpam-393	615	5	do	do	VERB
ejpam-393	615	6	to	to	PART
ejpam-393	615	7	follow	follow	VERB
ejpam-393	615	8	the	the	DET
ejpam-393	615	9	rule	rule	NOUN
ejpam-393	615	10	is	be	AUX
ejpam-393	615	11	:	:	PUNCT
ejpam-393	615	12	choose	choose	VERB
ejpam-393	615	13	i(a	i(a	NOUN
ejpam-393	615	14	)	)	PUNCT
ejpam-393	615	15	whenever	whenever	SCONJ
ejpam-393	615	16	player	player	NOUN
ejpam-393	615	17	∀	∀	NOUN
ejpam-393	615	18	has	have	AUX
ejpam-393	615	19	just	just	ADV
ejpam-393	615	20	chosen	choose	VERB
ejpam-393	615	21	an	an	DET
ejpam-393	615	22	element	element	NOUN
ejpam-393	615	23	a	a	PRON
ejpam-393	615	24	of	of	ADP
ejpam-393	615	25	a	a	PRON
ejpam-393	615	26	and	and	CCONJ
ejpam-393	615	27	i−1(b	i−1(b	ADJ
ejpam-393	615	28	)	)	PUNCT
ejpam-393	615	29	whenever	whenever	SCONJ
ejpam-393	615	30	player	player	NOUN
ejpam-393	615	31	∀	∀	NOUN
ejpam-393	615	32	has	have	AUX
ejpam-393	615	33	just	just	ADV
ejpam-393	615	34	chosen	choose	VERB
ejpam-393	615	35	b	b	PROPN
ejpam-393	615	36	from	from	ADP
ejpam-393	615	37	b.	b.	PROPN
ejpam-393	615	38	we	we	PRON
ejpam-393	615	39	write	write	VERB
ejpam-393	615	40	a	a	DET
ejpam-393	615	41	∼k	∼k	PROPN
ejpam-393	615	42	b	b	NOUN
ejpam-393	615	43	if	if	SCONJ
ejpam-393	615	44	∃	∃	PROPN
ejpam-393	615	45	can	can	AUX
ejpam-393	615	46	win	win	VERB
ejpam-393	615	47	efk(a	efk(a	PROPN
ejpam-393	615	48	,	,	PUNCT
ejpam-393	615	49	b	b	NOUN
ejpam-393	615	50	)	)	PUNCT
ejpam-393	615	51	.	.	PUNCT
ejpam-393	616	1	lemma	lemma	PROPN
ejpam-393	616	2	6	6	NUM
ejpam-393	616	3	.	.	PUNCT
ejpam-393	617	1	let	let	VERB
ejpam-393	617	2	l	l	NOUN
ejpam-393	617	3	be	be	AUX
ejpam-393	617	4	a	a	DET
ejpam-393	617	5	first	first	ADJ
ejpam-393	617	6	order	order	NOUN
ejpam-393	617	7	language	language	NOUN
ejpam-393	617	8	with	with	ADP
ejpam-393	617	9	finite	finite	ADJ
ejpam-393	617	10	signature	signature	NOUN
ejpam-393	617	11	.	.	PUNCT
ejpam-393	618	1	then	then	ADV
ejpam-393	618	2	for	for	ADP
ejpam-393	618	3	any	any	DET
ejpam-393	618	4	two	two	NUM
ejpam-393	618	5	l	l	NOUN
ejpam-393	618	6	structures	structure	NOUN
ejpam-393	618	7	a	a	PRON
ejpam-393	618	8	and	and	CCONJ
ejpam-393	618	9	b	b	NOUN
ejpam-393	618	10	the	the	DET
ejpam-393	618	11	following	following	NOUN
ejpam-393	618	12	are	be	AUX
ejpam-393	618	13	equivalent	equivalent	ADJ
ejpam-393	618	14	(	(	PUNCT
ejpam-393	618	15	i	i	NOUN
ejpam-393	618	16	)	)	PUNCT
ejpam-393	618	17	a	a	DET
ejpam-393	618	18	≡b	≡b	NOUN
ejpam-393	618	19	(	(	PUNCT
ejpam-393	618	20	ii	ii	NOUN
ejpam-393	618	21	)	)	PUNCT
ejpam-393	618	22	a	a	DET
ejpam-393	618	23	∼k	∼k	PROPN
ejpam-393	618	24	b	b	PROPN
ejpam-393	618	25	for	for	ADP
ejpam-393	618	26	all	all	PRON
ejpam-393	618	27	k	k	PROPN
ejpam-393	618	28	<	<	X
ejpam-393	618	29	ω	ω	PROPN
ejpam-393	618	30	.	.	PUNCT
ejpam-393	618	31	proof	proof	NOUN
ejpam-393	618	32	.	.	PUNCT
ejpam-393	619	1	[	[	X
ejpam-393	619	2	sketch	sketch	X
ejpam-393	619	3	]	]	X
ejpam-393	619	4	a	a	PRON
ejpam-393	619	5	and	and	CCONJ
ejpam-393	619	6	b	b	NOUN
ejpam-393	619	7	agree	agree	VERB
ejpam-393	619	8	on	on	ADP
ejpam-393	619	9	all	all	DET
ejpam-393	619	10	unnested	unnested	ADJ
ejpam-393	619	11	sentences	sentence	NOUN
ejpam-393	619	12	of	of	ADP
ejpam-393	619	13	finite	finite	ADJ
ejpam-393	619	14	quantifier	quantifier	NOUN
ejpam-393	619	15	rank	rank	NOUN
ejpam-393	619	16	,	,	PUNCT
ejpam-393	619	17	so	so	CCONJ
ejpam-393	619	18	(	(	PUNCT
ejpam-393	619	19	i	i	NOUN
ejpam-393	619	20	)	)	PUNCT
ejpam-393	619	21	implies	imply	VERB
ejpam-393	619	22	(	(	PUNCT
ejpam-393	619	23	ii	ii	NOUN
ejpam-393	619	24	)	)	PUNCT
ejpam-393	619	25	.	.	PUNCT
ejpam-393	620	1	the	the	DET
ejpam-393	620	2	other	other	ADJ
ejpam-393	620	3	direction	direction	NOUN
ejpam-393	620	4	follows	follow	VERB
ejpam-393	620	5	from	from	ADP
ejpam-393	620	6	the	the	DET
ejpam-393	620	7	fact	fact	NOUN
ejpam-393	620	8	that	that	SCONJ
ejpam-393	620	9	every	every	DET
ejpam-393	620	10	first	first	ADJ
ejpam-393	620	11	order	order	NOUN
ejpam-393	620	12	sentence	sentence	NOUN
ejpam-393	620	13	is	be	AUX
ejpam-393	620	14	equivalent	equivalent	ADJ
ejpam-393	620	15	to	to	ADP
ejpam-393	620	16	an	an	DET
ejpam-393	620	17	unnested	unnested	ADJ
ejpam-393	620	18	sentence	sentence	NOUN
ejpam-393	620	19	of	of	ADP
ejpam-393	620	20	finite	finite	PROPN
ejpam-393	620	21	quantifier	quantifier	NOUN
ejpam-393	620	22	rank	rank	NOUN
ejpam-393	620	23	.	.	PUNCT
ejpam-393	621	1	a	a	DET
ejpam-393	621	2	strategy	strategy	NOUN
ejpam-393	621	3	for	for	ADP
ejpam-393	621	4	a	a	DET
ejpam-393	621	5	player	player	NOUN
ejpam-393	621	6	in	in	ADP
ejpam-393	621	7	a	a	DET
ejpam-393	621	8	game	game	NOUN
ejpam-393	621	9	is	be	AUX
ejpam-393	621	10	a	a	DET
ejpam-393	621	11	set	set	NOUN
ejpam-393	621	12	of	of	ADP
ejpam-393	621	13	rules	rule	NOUN
ejpam-393	621	14	which	which	PRON
ejpam-393	621	15	tell	tell	VERB
ejpam-393	621	16	the	the	DET
ejpam-393	621	17	player	player	NOUN
ejpam-393	621	18	exactly	exactly	ADV
ejpam-393	621	19	how	how	SCONJ
ejpam-393	621	20	to	to	PART
ejpam-393	621	21	move	move	VERB
ejpam-393	621	22	,	,	PUNCT
ejpam-393	621	23	depending	depend	VERB
ejpam-393	621	24	on	on	ADP
ejpam-393	621	25	what	what	PRON
ejpam-393	621	26	has	have	AUX
ejpam-393	621	27	happened	happen	VERB
ejpam-393	621	28	earlier	early	ADV
ejpam-393	621	29	in	in	ADP
ejpam-393	621	30	the	the	DET
ejpam-393	621	31	play	play	NOUN
ejpam-393	621	32	.	.	PUNCT
ejpam-393	622	1	we	we	PRON
ejpam-393	622	2	say	say	VERB
ejpam-393	622	3	that	that	SCONJ
ejpam-393	622	4	the	the	DET
ejpam-393	622	5	player	player	NOUN
ejpam-393	622	6	uses	use	VERB
ejpam-393	622	7	the	the	DET
ejpam-393	622	8	strategy	strategy	NOUN
ejpam-393	622	9	σ	σ	NOUN
ejpam-393	622	10	in	in	ADP
ejpam-393	622	11	a	a	DET
ejpam-393	622	12	play	play	NOUN
ejpam-393	622	13	if	if	SCONJ
ejpam-393	622	14	each	each	PRON
ejpam-393	622	15	of	of	ADP
ejpam-393	622	16	his	his	PRON
ejpam-393	622	17	or	or	CCONJ
ejpam-393	622	18	her	her	PRON
ejpam-393	622	19	moves	move	NOUN
ejpam-393	622	20	obeys	obey	VERB
ejpam-393	622	21	the	the	DET
ejpam-393	622	22	rules	rule	NOUN
ejpam-393	622	23	of	of	ADP
ejpam-393	622	24	σ	σ	PROPN
ejpam-393	622	25	.	.	PUNCT
ejpam-393	623	1	we	we	PRON
ejpam-393	623	2	say	say	VERB
ejpam-393	623	3	that	that	SCONJ
ejpam-393	623	4	σ	σ	PROPN
ejpam-393	623	5	is	be	AUX
ejpam-393	623	6	a	a	DET
ejpam-393	623	7	winning	win	VERB
ejpam-393	623	8	strategy	strategy	NOUN
ejpam-393	623	9	if	if	SCONJ
ejpam-393	623	10	the	the	DET
ejpam-393	623	11	player	player	NOUN
ejpam-393	623	12	wins	win	VERB
ejpam-393	623	13	every	every	DET
ejpam-393	623	14	play	play	NOUN
ejpam-393	623	15	in	in	ADP
ejpam-393	623	16	which	which	PRON
ejpam-393	623	17	he	he	PRON
ejpam-393	623	18	or	or	CCONJ
ejpam-393	623	19	she	she	PRON
ejpam-393	623	20	uses	use	VERB
ejpam-393	623	21	σ	σ	X
ejpam-393	623	22	.	.	PUNCT
ejpam-393	624	1	we	we	PRON
ejpam-393	624	2	now	now	ADV
ejpam-393	624	3	have	have	VERB
ejpam-393	624	4	lemma	lemma	PROPN
ejpam-393	624	5	7	7	NUM
ejpam-393	624	6	.	.	PUNCT
ejpam-393	625	1	let	let	VERB
ejpam-393	625	2	b1	b1	NOUN
ejpam-393	625	3	,	,	PUNCT
ejpam-393	625	4	b2	b2	NOUN
ejpam-393	625	5	and	and	CCONJ
ejpam-393	625	6	b	b	NOUN
ejpam-393	625	7	be	be	AUX
ejpam-393	625	8	boolean	boolean	ADJ
ejpam-393	625	9	algebras	algebra	NOUN
ejpam-393	625	10	.	.	PUNCT
ejpam-393	626	1	assume	assume	VERB
ejpam-393	626	2	that	that	SCONJ
ejpam-393	626	3	b1	b1	PROPN
ejpam-393	626	4	≡	≡	PROPN
ejpam-393	626	5	b2	b2	NOUN
ejpam-393	626	6	,	,	PUNCT
ejpam-393	626	7	then	then	ADV
ejpam-393	626	8	b1	b1	NOUN
ejpam-393	626	9	×b	×b	NOUN
ejpam-393	626	10	≡	≡	PROPN
ejpam-393	626	11	b2	b2	NOUN
ejpam-393	626	12	×b	×b	NOUN
ejpam-393	626	13	.	.	PUNCT
ejpam-393	627	1	proof	proof	NOUN
ejpam-393	627	2	.	.	PUNCT
ejpam-393	628	1	it	it	PRON
ejpam-393	628	2	suffices	suffice	VERB
ejpam-393	628	3	to	to	PART
ejpam-393	628	4	show	show	VERB
ejpam-393	628	5	that	that	SCONJ
ejpam-393	628	6	if	if	SCONJ
ejpam-393	628	7	k	k	PROPN
ejpam-393	628	8	<	<	X
ejpam-393	628	9	ω	ω	PROPN
ejpam-393	628	10	and	and	CCONJ
ejpam-393	628	11	b1	b1	ADJ
ejpam-393	628	12	∼k	∼k	PROPN
ejpam-393	628	13	b2	b2	NOUN
ejpam-393	628	14	then	then	ADV
ejpam-393	628	15	b1	b1	NOUN
ejpam-393	628	16	×b	×b	ADJ
ejpam-393	628	17	∼k	∼k	PROPN
ejpam-393	628	18	b2	b2	NOUN
ejpam-393	628	19	×b	×b	NOUN
ejpam-393	628	20	.	.	PUNCT
ejpam-393	629	1	assume	assume	VERB
ejpam-393	629	2	henceforth	henceforth	ADV
ejpam-393	629	3	that	that	PRON
ejpam-393	629	4	b1	b1	VERB
ejpam-393	629	5	∼k	∼k	PROPN
ejpam-393	629	6	b2	b2	NOUN
ejpam-393	629	7	.	.	PUNCT
ejpam-393	630	1	then	then	ADV
ejpam-393	630	2	∃	∃	PROPN
ejpam-393	630	3	has	have	VERB
ejpam-393	630	4	a	a	DET
ejpam-393	630	5	winning	win	VERB
ejpam-393	630	6	strategy	strategy	NOUN
ejpam-393	630	7	σ	σ	NOUN
ejpam-393	630	8	for	for	ADP
ejpam-393	630	9	the	the	DET
ejpam-393	630	10	game	game	NOUN
ejpam-393	630	11	efk(b1,b2	efk(b1,b2	PROPN
ejpam-393	630	12	)	)	PUNCT
ejpam-393	630	13	.	.	PUNCT
ejpam-393	631	1	let	let	VERB
ejpam-393	631	2	the	the	DET
ejpam-393	631	3	two	two	NUM
ejpam-393	631	4	players	player	NOUN
ejpam-393	631	5	play	play	VERB
ejpam-393	631	6	the	the	DET
ejpam-393	631	7	game	game	NOUN
ejpam-393	631	8	efk(b1	efk(b1	VERB
ejpam-393	631	9	×b	×b	NOUN
ejpam-393	631	10	,	,	PUNCT
ejpam-393	631	11	b2	b2	NOUN
ejpam-393	631	12	×b	×b	NOUN
ejpam-393	631	13	)	)	PUNCT
ejpam-393	631	14	.	.	PUNCT
ejpam-393	632	1	∃	∃	PROPN
ejpam-393	632	2	guides	guide	VERB
ejpam-393	632	3	her	her	PRON
ejpam-393	632	4	choices	choice	NOUN
ejpam-393	632	5	by	by	ADP
ejpam-393	632	6	the	the	DET
ejpam-393	632	7	side	side	ADJ
ejpam-393	632	8	game	game	NOUN
ejpam-393	632	9	efk(b1,b2	efk(b1,b2	PROPN
ejpam-393	632	10	)	)	PUNCT
ejpam-393	632	11	.	.	PUNCT
ejpam-393	633	1	whenever	whenever	SCONJ
ejpam-393	633	2	∀	∀	PRON
ejpam-393	633	3	offers	offer	VERB
ejpam-393	633	4	an	an	DET
ejpam-393	633	5	element	element	NOUN
ejpam-393	633	6	,	,	PUNCT
ejpam-393	633	7	say	say	VERB
ejpam-393	633	8	the	the	DET
ejpam-393	633	9	element	element	NOUN
ejpam-393	633	10	a	a	DET
ejpam-393	633	11	∈	∈	PROPN
ejpam-393	633	12	b1	b1	NOUN
ejpam-393	633	13	×	×	PROPN
ejpam-393	633	14	b	b	PROPN
ejpam-393	633	15	,	,	PUNCT
ejpam-393	633	16	player	player	NOUN
ejpam-393	633	17	∃	∃	PROPN
ejpam-393	633	18	first	first	ADV
ejpam-393	633	19	splits	split	VERB
ejpam-393	633	20	it	it	PRON
ejpam-393	633	21	into	into	ADP
ejpam-393	633	22	a	a	DET
ejpam-393	633	23	product	product	NOUN
ejpam-393	633	24	a	a	DET
ejpam-393	633	25	=	=	PUNCT
ejpam-393	633	26	(	(	PUNCT
ejpam-393	633	27	g	g	NOUN
ejpam-393	633	28	,	,	PUNCT
ejpam-393	633	29	h	h	NOUN
ejpam-393	633	30	)	)	PUNCT
ejpam-393	633	31	with	with	ADP
ejpam-393	633	32	g	g	PROPN
ejpam-393	633	33	∈	∈	PROPN
ejpam-393	633	34	b1	b1	NOUN
ejpam-393	633	35	and	and	CCONJ
ejpam-393	633	36	h	h	NOUN
ejpam-393	633	37	∈	∈	PROPN
ejpam-393	633	38	b.	b.	PROPN
ejpam-393	634	1	then	then	ADV
ejpam-393	634	2	she	she	PRON
ejpam-393	634	3	pretends	pretend	VERB
ejpam-393	634	4	that	that	SCONJ
ejpam-393	634	5	∀	∀	PUNCT
ejpam-393	634	6	has	have	AUX
ejpam-393	634	7	chosen	choose	VERB
ejpam-393	634	8	g	g	NOUN
ejpam-393	634	9	in	in	ADP
ejpam-393	634	10	the	the	DET
ejpam-393	634	11	side	side	NOUN
ejpam-393	634	12	game	game	NOUN
ejpam-393	634	13	.	.	PUNCT
ejpam-393	635	1	she	she	PRON
ejpam-393	635	2	uses	use	VERB
ejpam-393	635	3	her	her	PRON
ejpam-393	635	4	strategy	strategy	NOUN
ejpam-393	635	5	σ	σ	NOUN
ejpam-393	635	6	to	to	PART
ejpam-393	635	7	choose	choose	VERB
ejpam-393	635	8	a	a	DET
ejpam-393	635	9	reply	reply	NOUN
ejpam-393	635	10	g′	g′	NOUN
ejpam-393	635	11	of	of	ADP
ejpam-393	635	12	g	g	PROPN
ejpam-393	635	13	in	in	ADP
ejpam-393	635	14	the	the	DET
ejpam-393	635	15	side	side	NOUN
ejpam-393	635	16	game	game	NOUN
ejpam-393	635	17	.	.	PUNCT
ejpam-393	636	1	her	her	PRON
ejpam-393	636	2	reply	reply	NOUN
ejpam-393	636	3	to	to	ADP
ejpam-393	636	4	the	the	DET
ejpam-393	636	5	element	element	NOUN
ejpam-393	636	6	a	a	PRON
ejpam-393	636	7	will	will	AUX
ejpam-393	636	8	be	be	AUX
ejpam-393	636	9	the	the	DET
ejpam-393	636	10	element	element	NOUN
ejpam-393	636	11	b	b	PROPN
ejpam-393	636	12	=	=	SYM
ejpam-393	636	13	(	(	PUNCT
ejpam-393	636	14	g′,h	g′,h	PROPN
ejpam-393	636	15	)	)	PUNCT
ejpam-393	636	16	∈	∈	PROPN
ejpam-393	636	17	b2	b2	NOUN
ejpam-393	636	18	×	×	PROPN
ejpam-393	636	19	b.	b.	NOUN
ejpam-393	636	20	at	at	ADP
ejpam-393	636	21	the	the	DET
ejpam-393	636	22	end	end	NOUN
ejpam-393	636	23	of	of	ADP
ejpam-393	636	24	the	the	DET
ejpam-393	636	25	game	game	NOUN
ejpam-393	636	26	t.	t.	PROPN
ejpam-393	636	27	ahmed	ahmed	PROPN
ejpam-393	636	28	/	/	SYM
ejpam-393	636	29	eur	eur	PROPN
ejpam-393	636	30	.	.	PUNCT
ejpam-393	637	1	j.	j.	PROPN
ejpam-393	637	2	pure	pure	PROPN
ejpam-393	637	3	appl	appl	PROPN
ejpam-393	637	4	.	.	PROPN
ejpam-393	637	5	math	math	PROPN
ejpam-393	637	6	,	,	PUNCT
ejpam-393	637	7	3	3	NUM
ejpam-393	637	8	(	(	PUNCT
ejpam-393	637	9	2010	2010	NUM
ejpam-393	637	10	)	)	PUNCT
ejpam-393	637	11	,	,	PUNCT
ejpam-393	637	12	853	853	NUM
ejpam-393	637	13	-	-	SYM
ejpam-393	637	14	880	880	NUM
ejpam-393	637	15	867	867	NUM
ejpam-393	637	16	let	let	VERB
ejpam-393	637	17	the	the	DET
ejpam-393	637	18	play	play	NOUN
ejpam-393	637	19	be	be	AUX
ejpam-393	637	20	(	(	PUNCT
ejpam-393	637	21	(	(	PUNCT
ejpam-393	637	22	g0,h0	g0,h0	PROPN
ejpam-393	637	23	)	)	PUNCT
ejpam-393	637	24	,	,	PUNCT
ejpam-393	637	25	.	.	PUNCT
ejpam-393	637	26	.	.	PUNCT
ejpam-393	637	27	.	.	PUNCT
ejpam-393	638	1	(	(	PUNCT
ejpam-393	638	2	gk−1,hk−1	gk−1,hk−1	NOUN
ejpam-393	638	3	)	)	PUNCT
ejpam-393	638	4	;	;	PUNCT
ejpam-393	638	5	(	(	PUNCT
ejpam-393	638	6	g	g	NOUN
ejpam-393	638	7	′	′	NUM
ejpam-393	638	8	0,h′0	0,h′0	NUM
ejpam-393	638	9	)	)	PUNCT
ejpam-393	638	10	,	,	PUNCT
ejpam-393	638	11	.	.	PUNCT
ejpam-393	638	12	.	.	PUNCT
ejpam-393	638	13	.	.	PUNCT
ejpam-393	639	1	(	(	PUNCT
ejpam-393	639	2	g	g	NOUN
ejpam-393	639	3	′	′	NUM
ejpam-393	639	4	k−1	k−1	PROPN
ejpam-393	639	5	,	,	PUNCT
ejpam-393	639	6	h′	h′	PROPN
ejpam-393	639	7	k−1	k−1	PROPN
ejpam-393	639	8	)	)	PUNCT
ejpam-393	639	9	)	)	PUNCT
ejpam-393	639	10	.	.	PUNCT
ejpam-393	640	1	player	player	NOUN
ejpam-393	640	2	∃	∃	PROPN
ejpam-393	640	3	has	have	AUX
ejpam-393	640	4	won	win	VERB
ejpam-393	640	5	the	the	DET
ejpam-393	640	6	side	side	NOUN
ejpam-393	640	7	game	game	NOUN
ejpam-393	640	8	.	.	PUNCT
ejpam-393	641	1	now	now	ADV
ejpam-393	641	2	the	the	DET
ejpam-393	641	3	unnested	unnested	ADJ
ejpam-393	641	4	atomic	atomic	ADJ
ejpam-393	641	5	formulas	formula	NOUN
ejpam-393	641	6	of	of	ADP
ejpam-393	641	7	boolean	boolean	ADJ
ejpam-393	641	8	algebras	algebra	NOUN
ejpam-393	641	9	are	be	AUX
ejpam-393	641	10	of	of	ADP
ejpam-393	641	11	the	the	DET
ejpam-393	641	12	form	form	NOUN
ejpam-393	641	13	x	x	PUNCT
ejpam-393	641	14	=	=	SYM
ejpam-393	641	15	y	y	PROPN
ejpam-393	641	16	,	,	PUNCT
ejpam-393	641	17	1	1	NUM
ejpam-393	641	18	=	=	SYM
ejpam-393	641	19	x	x	X
ejpam-393	641	20	,	,	PUNCT
ejpam-393	641	21	0=	0=	NUM
ejpam-393	641	22	x	x	SYM
ejpam-393	641	23	,	,	PUNCT
ejpam-393	642	1	x0	x0	PROPN
ejpam-393	642	2	∧	∧	PROPN
ejpam-393	642	3	x1	x1	PROPN
ejpam-393	642	4	=	=	SYM
ejpam-393	642	5	y	y	PROPN
ejpam-393	642	6	,	,	PUNCT
ejpam-393	642	7	x0	x0	PROPN
ejpam-393	642	8	∨	∨	NUM
ejpam-393	642	9	x1	x1	PROPN
ejpam-393	642	10	=	=	SYM
ejpam-393	642	11	y	y	PROPN
ejpam-393	642	12	and	and	CCONJ
ejpam-393	642	13	−x	−x	NOUN
ejpam-393	642	14	=	=	PUNCT
ejpam-393	643	1	y.	y.	NOUN
ejpam-393	643	2	so	so	ADV
ejpam-393	643	3	for	for	ADP
ejpam-393	643	4	i	i	PROPN
ejpam-393	643	5	,	,	PUNCT
ejpam-393	643	6	j	j	PROPN
ejpam-393	643	7	,	,	PUNCT
ejpam-393	644	1	l	l	NOUN
ejpam-393	644	2	<	<	X
ejpam-393	644	3	k	k	X
ejpam-393	644	4	we	we	PRON
ejpam-393	644	5	have	have	AUX
ejpam-393	644	6	gi	gi	VERB
ejpam-393	644	7	=	=	PUNCT
ejpam-393	645	1	g	g	PROPN
ejpam-393	645	2	j	j	PROPN
ejpam-393	645	3	iff	iff	PROPN
ejpam-393	645	4	g′i	g′i	VERB
ejpam-393	645	5	=	=	SYM
ejpam-393	645	6	g′j	g′j	NOUN
ejpam-393	645	7	1=	1=	X
ejpam-393	645	8	gi	gi	ADP
ejpam-393	645	9	iff	iff	PROPN
ejpam-393	645	10	1=	1=	X
ejpam-393	645	11	g′i	g′i	VERB
ejpam-393	646	1	0=	0=	NOUN
ejpam-393	646	2	gi	gi	PROPN
ejpam-393	646	3	iff	iff	PROPN
ejpam-393	646	4	0=	0=	PROPN
ejpam-393	646	5	g′i	g′i	VERB
ejpam-393	646	6	gi	gi	ADP
ejpam-393	646	7	∧	∧	PROPN
ejpam-393	646	8	g	g	PROPN
ejpam-393	646	9	j	j	PROPN
ejpam-393	646	10	=	=	PROPN
ejpam-393	646	11	gl	gl	PROPN
ejpam-393	646	12	iff	iff	PROPN
ejpam-393	646	13	g′i	g′i	VERB
ejpam-393	646	14	∧	∧	NOUN
ejpam-393	646	15	g′j	g′j	NOUN
ejpam-393	646	16	=	=	SYM
ejpam-393	646	17	g′l	g′l	PROPN
ejpam-393	646	18	gi	gi	NOUN
ejpam-393	646	19	∨	∨	NOUN
ejpam-393	646	20	gi	gi	VERB
ejpam-393	646	21	=	=	SYM
ejpam-393	646	22	gl	gl	PROPN
ejpam-393	646	23	iff	iff	PROPN
ejpam-393	646	24	g′i	g′i	VERB
ejpam-393	646	25	∧	∧	NOUN
ejpam-393	646	26	g′j	g′j	NOUN
ejpam-393	646	27	=	=	PUNCT
ejpam-393	646	28	g′	g′	NOUN
ejpam-393	646	29	l	l	NOUN
ejpam-393	646	30	−gi	−gi	NOUN
ejpam-393	646	31	=	=	SYM
ejpam-393	646	32	g	g	PROPN
ejpam-393	646	33	j	j	PROPN
ejpam-393	646	34	iff	iff	PROPN
ejpam-393	646	35	−	−	PROPN
ejpam-393	646	36	g′i	g′i	VERB
ejpam-393	646	37	=	=	SYM
ejpam-393	646	38	g′j	g′j	NOUN
ejpam-393	646	39	.	.	PUNCT
ejpam-393	647	1	by	by	ADP
ejpam-393	647	2	the	the	DET
ejpam-393	647	3	cartesian	cartesian	ADJ
ejpam-393	647	4	product	product	NOUN
ejpam-393	647	5	for	for	ADP
ejpam-393	647	6	boolean	boolean	ADJ
ejpam-393	647	7	algebras	algebra	NOUN
ejpam-393	647	8	,	,	PUNCT
ejpam-393	647	9	this	this	PRON
ejpam-393	647	10	implies	imply	VERB
ejpam-393	647	11	that	that	SCONJ
ejpam-393	647	12	for	for	ADP
ejpam-393	647	13	all	all	DET
ejpam-393	647	14	i	i	PROPN
ejpam-393	647	15	,	,	PUNCT
ejpam-393	647	16	j	j	PROPN
ejpam-393	647	17	,	,	PUNCT
ejpam-393	647	18	l	l	NOUN
ejpam-393	647	19	<	<	X
ejpam-393	647	20	k	k	X
ejpam-393	647	21	we	we	PRON
ejpam-393	647	22	also	also	ADV
ejpam-393	647	23	have	have	VERB
ejpam-393	647	24	(	(	PUNCT
ejpam-393	647	25	gi	gi	INTJ
ejpam-393	647	26	,	,	PUNCT
ejpam-393	647	27	hi	hi	INTJ
ejpam-393	647	28	)	)	PUNCT
ejpam-393	647	29	=	=	SYM
ejpam-393	648	1	(	(	PUNCT
ejpam-393	648	2	g	g	PROPN
ejpam-393	648	3	j	j	PROPN
ejpam-393	648	4	,	,	PUNCT
ejpam-393	648	5	h	h	PROPN
ejpam-393	648	6	j	j	PROPN
ejpam-393	648	7	)	)	PUNCT
ejpam-393	648	8	iff	iff	PROPN
ejpam-393	648	9	(	(	PUNCT
ejpam-393	648	10	g′i	g′i	PROPN
ejpam-393	648	11	,	,	PUNCT
ejpam-393	648	12	hi	hi	INTJ
ejpam-393	648	13	)	)	PUNCT
ejpam-393	648	14	=	=	SYM
ejpam-393	648	15	(	(	PUNCT
ejpam-393	648	16	g	g	PROPN
ejpam-393	648	17	′	′	NUM
ejpam-393	648	18	j	j	PROPN
ejpam-393	648	19	,	,	PUNCT
ejpam-393	648	20	hi	hi	INTJ
ejpam-393	648	21	)	)	PUNCT
ejpam-393	648	22	1=	1=	X
ejpam-393	648	23	(	(	PUNCT
ejpam-393	648	24	gi	gi	INTJ
ejpam-393	648	25	,	,	PUNCT
ejpam-393	648	26	hi	hi	ADJ
ejpam-393	648	27	)	)	PUNCT
ejpam-393	648	28	iff	iff	VERB
ejpam-393	648	29	1=	1=	X
ejpam-393	648	30	(	(	PUNCT
ejpam-393	648	31	g′i	g′i	VERB
ejpam-393	648	32	,	,	PUNCT
ejpam-393	648	33	hi	hi	ADJ
ejpam-393	648	34	)	)	PUNCT
ejpam-393	648	35	same	same	ADJ
ejpam-393	648	36	for	for	ADP
ejpam-393	648	37	0	0	NUM
ejpam-393	648	38	0=	0=	NUM
ejpam-393	649	1	(	(	PUNCT
ejpam-393	649	2	gi	gi	INTJ
ejpam-393	649	3	,	,	PUNCT
ejpam-393	649	4	hi	hi	ADJ
ejpam-393	649	5	)	)	PUNCT
ejpam-393	649	6	iff	iff	PROPN
ejpam-393	649	7	0=	0=	PRON
ejpam-393	649	8	(	(	PUNCT
ejpam-393	649	9	g′i	g′i	VERB
ejpam-393	649	10	,	,	PUNCT
ejpam-393	649	11	hi	hi	INTJ
ejpam-393	649	12	)	)	PUNCT
ejpam-393	649	13	(	(	PUNCT
ejpam-393	649	14	gi	gi	INTJ
ejpam-393	649	15	∧	∧	PROPN
ejpam-393	650	1	hi	hi	INTJ
ejpam-393	650	2	,	,	PUNCT
ejpam-393	650	3	g	g	PROPN
ejpam-393	650	4	j	j	PROPN
ejpam-393	650	5	∧	∧	PROPN
ejpam-393	650	6	h	h	PROPN
ejpam-393	650	7	j	j	NOUN
ejpam-393	650	8	)	)	PUNCT
ejpam-393	650	9	=	=	PRON
ejpam-393	650	10	(	(	PUNCT
ejpam-393	650	11	gl	gl	INTJ
ejpam-393	650	12	,	,	PUNCT
ejpam-393	650	13	hl	hl	PROPN
ejpam-393	650	14	)	)	PUNCT
ejpam-393	650	15	iff	iff	PROPN
ejpam-393	650	16	(	(	PUNCT
ejpam-393	650	17	g′i	g′i	VERB
ejpam-393	650	18	∧	∧	PROPN
ejpam-393	650	19	hi	hi	INTJ
ejpam-393	650	20	,	,	PUNCT
ejpam-393	650	21	g′j	g′j	VERB
ejpam-393	650	22	∧	∧	PROPN
ejpam-393	650	23	h	h	NOUN
ejpam-393	650	24	j	j	NOUN
ejpam-393	650	25	)	)	PUNCT
ejpam-393	650	26	=	=	PUNCT
ejpam-393	651	1	(	(	PUNCT
ejpam-393	651	2	g	g	PROPN
ejpam-393	651	3	′	′	NUM
ejpam-393	651	4	l	l	NOUN
ejpam-393	651	5	,	,	PUNCT
ejpam-393	651	6	hl	hl	NOUN
ejpam-393	651	7	)	)	PUNCT
ejpam-393	651	8	(	(	PUNCT
ejpam-393	651	9	gi	gi	PROPN
ejpam-393	651	10	∨	∨	NUM
ejpam-393	651	11	hi	hi	INTJ
ejpam-393	651	12	,	,	PUNCT
ejpam-393	651	13	g	g	PROPN
ejpam-393	651	14	j	j	PROPN
ejpam-393	651	15	∨	∨	NUM
ejpam-393	651	16	h	h	PROPN
ejpam-393	651	17	j	j	PROPN
ejpam-393	651	18	)	)	PUNCT
ejpam-393	651	19	=	=	SYM
ejpam-393	651	20	(	(	PUNCT
ejpam-393	651	21	gl	gl	INTJ
ejpam-393	651	22	,	,	PUNCT
ejpam-393	651	23	hl	hl	PROPN
ejpam-393	651	24	)	)	PUNCT
ejpam-393	651	25	iff	iff	PROPN
ejpam-393	651	26	(	(	PUNCT
ejpam-393	651	27	g′i	g′i	PROPN
ejpam-393	651	28	∨	∨	NUM
ejpam-393	651	29	hi	hi	ADJ
ejpam-393	651	30	,	,	PUNCT
ejpam-393	651	31	g′j	g′j	NOUN
ejpam-393	651	32	∨	∨	NUM
ejpam-393	651	33	h	h	PROPN
ejpam-393	651	34	j	j	PROPN
ejpam-393	651	35	)	)	PUNCT
ejpam-393	652	1	=	=	PUNCT
ejpam-393	652	2	(	(	PUNCT
ejpam-393	652	3	g	g	PROPN
ejpam-393	652	4	′	′	NUM
ejpam-393	652	5	l	l	NOUN
ejpam-393	652	6	,	,	PUNCT
ejpam-393	652	7	hl	hl	NOUN
ejpam-393	652	8	)	)	PUNCT
ejpam-393	653	1	−(gi	−(gi	PROPN
ejpam-393	653	2	,	,	PUNCT
ejpam-393	653	3	hi	hi	INTJ
ejpam-393	653	4	)	)	PUNCT
ejpam-393	653	5	=	=	SYM
ejpam-393	654	1	(	(	PUNCT
ejpam-393	654	2	g	g	PROPN
ejpam-393	654	3	j	j	PROPN
ejpam-393	654	4	,	,	PUNCT
ejpam-393	654	5	h	h	PROPN
ejpam-393	654	6	j	j	PROPN
ejpam-393	654	7	)	)	PUNCT
ejpam-393	654	8	iff	iff	PROPN
ejpam-393	654	9	−	−	PROPN
ejpam-393	654	10	(	(	PUNCT
ejpam-393	654	11	g′i	g′i	PROPN
ejpam-393	654	12	,	,	PUNCT
ejpam-393	654	13	hi	hi	INTJ
ejpam-393	654	14	)	)	PUNCT
ejpam-393	654	15	=	=	SYM
ejpam-393	655	1	(	(	PUNCT
ejpam-393	655	2	g	g	PROPN
ejpam-393	655	3	′	′	NUM
ejpam-393	655	4	j	j	PROPN
ejpam-393	655	5	,	,	PUNCT
ejpam-393	655	6	h	h	PROPN
ejpam-393	655	7	j	j	PROPN
ejpam-393	655	8	)	)	PUNCT
ejpam-393	655	9	.	.	PUNCT
ejpam-393	656	1	so	so	ADV
ejpam-393	656	2	∃	∃	PROPN
ejpam-393	656	3	wins	win	VERB
ejpam-393	656	4	the	the	DET
ejpam-393	656	5	game	game	NOUN
ejpam-393	656	6	,	,	PUNCT
ejpam-393	656	7	which	which	PRON
ejpam-393	656	8	proves	prove	VERB
ejpam-393	656	9	the	the	DET
ejpam-393	656	10	lemma	lemma	PROPN
ejpam-393	656	11	..	..	PUNCT
ejpam-393	656	12	definition	definition	NOUN
ejpam-393	656	13	9	9	NUM
ejpam-393	656	14	.	.	PUNCT
ejpam-393	657	1	(	(	PUNCT
ejpam-393	657	2	1	1	X
ejpam-393	657	3	)	)	PUNCT
ejpam-393	657	4	let	let	VERB
ejpam-393	657	5	l	l	NOUN
ejpam-393	657	6	be	be	AUX
ejpam-393	657	7	a	a	DET
ejpam-393	657	8	signature	signature	NOUN
ejpam-393	657	9	and	and	CCONJ
ejpam-393	657	10	d	d	ADP
ejpam-393	657	11	an	an	DET
ejpam-393	657	12	l	l	NOUN
ejpam-393	657	13	structure	structure	NOUN
ejpam-393	657	14	.	.	PUNCT
ejpam-393	658	1	the	the	DET
ejpam-393	658	2	age	age	NOUN
ejpam-393	658	3	of	of	ADP
ejpam-393	658	4	d	d	PROPN
ejpam-393	658	5	is	be	AUX
ejpam-393	658	6	the	the	DET
ejpam-393	658	7	class	class	NOUN
ejpam-393	658	8	k	k	PROPN
ejpam-393	658	9	of	of	ADP
ejpam-393	658	10	all	all	DET
ejpam-393	658	11	finitely	finitely	ADV
ejpam-393	658	12	generated	generate	VERB
ejpam-393	658	13	structures	structure	NOUN
ejpam-393	658	14	that	that	PRON
ejpam-393	658	15	can	can	AUX
ejpam-393	658	16	be	be	AUX
ejpam-393	658	17	embedded	embed	VERB
ejpam-393	658	18	in	in	ADP
ejpam-393	658	19	d.	d.	PROPN
ejpam-393	658	20	(	(	PUNCT
ejpam-393	658	21	2	2	NUM
ejpam-393	658	22	)	)	PUNCT
ejpam-393	658	23	a	a	DET
ejpam-393	658	24	class	class	NOUN
ejpam-393	658	25	k	k	PROPN
ejpam-393	658	26	is	be	AUX
ejpam-393	658	27	the	the	DET
ejpam-393	658	28	age	age	NOUN
ejpam-393	658	29	of	of	ADP
ejpam-393	658	30	d	d	PROPN
ejpam-393	658	31	if	if	SCONJ
ejpam-393	658	32	the	the	DET
ejpam-393	658	33	structures	structure	NOUN
ejpam-393	658	34	in	in	ADP
ejpam-393	658	35	k	k	PROPN
ejpam-393	658	36	are	be	AUX
ejpam-393	658	37	up	up	ADP
ejpam-393	658	38	to	to	ADP
ejpam-393	658	39	isomorphism	isomorphism	NOUN
ejpam-393	658	40	,	,	PUNCT
ejpam-393	658	41	exactly	exactly	ADV
ejpam-393	658	42	the	the	DET
ejpam-393	658	43	finitely	finitely	ADV
ejpam-393	658	44	generated	generate	VERB
ejpam-393	658	45	substructures	substructure	NOUN
ejpam-393	658	46	of	of	ADP
ejpam-393	658	47	d.	d.	PROPN
ejpam-393	658	48	(	(	PUNCT
ejpam-393	658	49	3	3	X
ejpam-393	658	50	)	)	PUNCT
ejpam-393	658	51	let	let	VERB
ejpam-393	658	52	k	k	PRON
ejpam-393	658	53	be	be	AUX
ejpam-393	658	54	a	a	DET
ejpam-393	658	55	class	class	NOUN
ejpam-393	658	56	of	of	ADP
ejpam-393	658	57	structures	structure	NOUN
ejpam-393	658	58	.	.	PUNCT
ejpam-393	659	1	(	(	PUNCT
ejpam-393	659	2	4	4	X
ejpam-393	659	3	)	)	PUNCT
ejpam-393	659	4	k	k	PROPN
ejpam-393	659	5	has	have	VERB
ejpam-393	659	6	the	the	DET
ejpam-393	659	7	hereditary	hereditary	ADJ
ejpam-393	659	8	property	property	NOUN
ejpam-393	659	9	,	,	PUNCT
ejpam-393	659	10	hp	hp	NOUN
ejpam-393	659	11	for	for	ADP
ejpam-393	659	12	short	short	ADJ
ejpam-393	659	13	.	.	PUNCT
ejpam-393	660	1	if	if	SCONJ
ejpam-393	660	2	whenever	whenever	SCONJ
ejpam-393	660	3	a	a	DET
ejpam-393	660	4	∈	∈	PROPN
ejpam-393	660	5	k	k	PROPN
ejpam-393	660	6	and	and	CCONJ
ejpam-393	660	7	b	b	PROPN
ejpam-393	660	8	is	be	AUX
ejpam-393	660	9	a	a	DET
ejpam-393	660	10	finitely	finitely	ADV
ejpam-393	660	11	generated	generate	VERB
ejpam-393	660	12	substructure	substructure	NOUN
ejpam-393	660	13	of	of	ADP
ejpam-393	660	14	a	a	DET
ejpam-393	660	15	then	then	ADV
ejpam-393	660	16	b	b	NOUN
ejpam-393	660	17	is	be	AUX
ejpam-393	660	18	isomorphic	isomorphic	ADJ
ejpam-393	660	19	to	to	ADP
ejpam-393	660	20	some	some	DET
ejpam-393	660	21	structure	structure	NOUN
ejpam-393	660	22	in	in	ADP
ejpam-393	660	23	k.	k.	PROPN
ejpam-393	660	24	(	(	PUNCT
ejpam-393	660	25	5	5	NUM
ejpam-393	660	26	)	)	PUNCT
ejpam-393	660	27	k	k	PROPN
ejpam-393	660	28	has	have	VERB
ejpam-393	660	29	the	the	DET
ejpam-393	660	30	joint	joint	ADJ
ejpam-393	660	31	embedding	embed	VERB
ejpam-393	660	32	property	property	NOUN
ejpam-393	660	33	,	,	PUNCT
ejpam-393	660	34	j	j	PROPN
ejpam-393	660	35	ep	ep	PROPN
ejpam-393	660	36	for	for	ADP
ejpam-393	660	37	short	short	ADJ
ejpam-393	660	38	if	if	SCONJ
ejpam-393	660	39	whenever	whenever	SCONJ
ejpam-393	660	40	a	a	PRON
ejpam-393	660	41	,	,	PUNCT
ejpam-393	660	42	b	b	X
ejpam-393	660	43	∈	∈	PROPN
ejpam-393	661	1	k	k	NOUN
ejpam-393	661	2	then	then	ADV
ejpam-393	661	3	there	there	PRON
ejpam-393	661	4	is	be	VERB
ejpam-393	661	5	a	a	DET
ejpam-393	661	6	c	c	NOUN
ejpam-393	661	7	∈	∈	PROPN
ejpam-393	661	8	k	k	NOUN
ejpam-393	661	9	such	such	ADJ
ejpam-393	661	10	that	that	SCONJ
ejpam-393	661	11	both	both	DET
ejpam-393	661	12	a	a	PRON
ejpam-393	661	13	and	and	CCONJ
ejpam-393	661	14	b	b	NOUN
ejpam-393	661	15	are	be	AUX
ejpam-393	661	16	embeddable	embeddable	ADJ
ejpam-393	661	17	in	in	ADP
ejpam-393	661	18	c.	c.	PROPN
ejpam-393	661	19	(	(	PUNCT
ejpam-393	661	20	6	6	NUM
ejpam-393	661	21	)	)	PUNCT
ejpam-393	661	22	k	k	PROPN
ejpam-393	661	23	has	have	AUX
ejpam-393	661	24	amalgamation	amalgamation	NOUN
ejpam-393	661	25	property	property	NOUN
ejpam-393	661	26	,	,	PUNCT
ejpam-393	661	27	or	or	CCONJ
ejpam-393	661	28	ap	ap	VERB
ejpam-393	661	29	for	for	ADP
ejpam-393	661	30	short	short	ADJ
ejpam-393	661	31	if	if	SCONJ
ejpam-393	661	32	a	a	DET
ejpam-393	661	33	,	,	PUNCT
ejpam-393	661	34	b	b	NOUN
ejpam-393	661	35	,	,	PUNCT
ejpam-393	661	36	c	c	PROPN
ejpam-393	661	37	∈	∈	PROPN
ejpam-393	661	38	k	k	PROPN
ejpam-393	661	39	and	and	CCONJ
ejpam-393	661	40	e	e	NOUN
ejpam-393	661	41	:	:	PUNCT
ejpam-393	661	42	a→	a→	PROPN
ejpam-393	661	43	b	b	X
ejpam-393	661	44	,	,	PUNCT
ejpam-393	661	45	f	f	X
ejpam-393	661	46	:	:	PUNCT
ejpam-393	661	47	a→	a→	PUNCT
ejpam-393	661	48	c	c	NOUN
ejpam-393	661	49	are	be	AUX
ejpam-393	661	50	embeddings	embedding	NOUN
ejpam-393	661	51	,	,	PUNCT
ejpam-393	661	52	then	then	ADV
ejpam-393	661	53	there	there	PRON
ejpam-393	661	54	are	be	VERB
ejpam-393	661	55	d	d	PROPN
ejpam-393	661	56	in	in	ADP
ejpam-393	661	57	k	k	NOUN
ejpam-393	661	58	and	and	CCONJ
ejpam-393	661	59	embeddings	embedding	VERB
ejpam-393	661	60	g	g	NOUN
ejpam-393	661	61	:	:	PUNCT
ejpam-393	661	62	b→	b→	PROPN
ejpam-393	661	63	d	d	PROPN
ejpam-393	661	64	and	and	CCONJ
ejpam-393	661	65	h	h	NOUN
ejpam-393	661	66	:	:	PUNCT
ejpam-393	662	1	c	c	X
ejpam-393	662	2	→	→	PUNCT
ejpam-393	662	3	d	d	X
ejpam-393	662	4	such	such	ADJ
ejpam-393	662	5	that	that	DET
ejpam-393	662	6	g	g	PROPN
ejpam-393	662	7	◦	◦	NOUN
ejpam-393	662	8	e	e	NOUN
ejpam-393	662	9	=	=	SYM
ejpam-393	662	10	h	h	PROPN
ejpam-393	662	11	◦	◦	NOUN
ejpam-393	662	12	f	f	X
ejpam-393	662	13	.	.	PUNCT
ejpam-393	663	1	t.	t.	PROPN
ejpam-393	663	2	ahmed	ahmed	PROPN
ejpam-393	663	3	/	/	SYM
ejpam-393	663	4	eur	eur	PROPN
ejpam-393	663	5	.	.	PUNCT
ejpam-393	664	1	j.	j.	PROPN
ejpam-393	664	2	pure	pure	PROPN
ejpam-393	664	3	appl	appl	PROPN
ejpam-393	664	4	.	.	PROPN
ejpam-393	664	5	math	math	PROPN
ejpam-393	664	6	,	,	PUNCT
ejpam-393	664	7	3	3	NUM
ejpam-393	664	8	(	(	PUNCT
ejpam-393	664	9	2010	2010	NUM
ejpam-393	664	10	)	)	PUNCT
ejpam-393	664	11	,	,	PUNCT
ejpam-393	664	12	853	853	NUM
ejpam-393	664	13	-	-	SYM
ejpam-393	664	14	880	880	NUM
ejpam-393	664	15	868	868	NUM
ejpam-393	664	16	(	(	PUNCT
ejpam-393	664	17	7	7	NUM
ejpam-393	664	18	)	)	PUNCT
ejpam-393	664	19	a	a	DET
ejpam-393	664	20	structure	structure	NOUN
ejpam-393	664	21	d	d	NOUN
ejpam-393	664	22	is	be	AUX
ejpam-393	664	23	weakly	weakly	ADV
ejpam-393	664	24	homogeneous	homogeneous	ADJ
ejpam-393	664	25	if	if	SCONJ
ejpam-393	664	26	it	it	PRON
ejpam-393	664	27	has	have	VERB
ejpam-393	664	28	the	the	DET
ejpam-393	664	29	the	the	DET
ejpam-393	664	30	following	follow	VERB
ejpam-393	664	31	property	property	NOUN
ejpam-393	664	32	if	if	SCONJ
ejpam-393	664	33	a	a	DET
ejpam-393	664	34	,	,	PUNCT
ejpam-393	664	35	b	b	NOUN
ejpam-393	664	36	are	be	AUX
ejpam-393	664	37	finitely	finitely	ADV
ejpam-393	664	38	generated	generate	VERB
ejpam-393	664	39	substructures	substructure	NOUN
ejpam-393	664	40	of	of	ADP
ejpam-393	664	41	d	d	PROPN
ejpam-393	664	42	,	,	PUNCT
ejpam-393	664	43	a⊆	a⊆	PROPN
ejpam-393	664	44	b	b	NOUN
ejpam-393	664	45	and	and	CCONJ
ejpam-393	664	46	f	f	NOUN
ejpam-393	664	47	:	:	PUNCT
ejpam-393	664	48	a→d	a→d	PRON
ejpam-393	664	49	is	be	AUX
ejpam-393	664	50	an	an	DET
ejpam-393	664	51	embedding	embedding	NOUN
ejpam-393	664	52	,	,	PUNCT
ejpam-393	664	53	then	then	ADV
ejpam-393	664	54	there	there	PRON
ejpam-393	664	55	is	be	VERB
ejpam-393	664	56	an	an	DET
ejpam-393	664	57	embedding	embed	VERB
ejpam-393	664	58	g	g	NOUN
ejpam-393	664	59	:	:	PUNCT
ejpam-393	664	60	b→d	b→d	ADJ
ejpam-393	664	61	which	which	PRON
ejpam-393	664	62	extends	extend	VERB
ejpam-393	664	63	f	f	PROPN
ejpam-393	664	64	.	.	PUNCT
ejpam-393	665	1	(	(	PUNCT
ejpam-393	665	2	8)	8)	NUM
ejpam-393	665	3	we	we	PRON
ejpam-393	665	4	call	call	VERB
ejpam-393	665	5	a	a	DET
ejpam-393	665	6	structure	structure	NOUN
ejpam-393	665	7	d	d	X
ejpam-393	665	8	homogeneous	homogeneous	ADJ
ejpam-393	665	9	if	if	SCONJ
ejpam-393	665	10	every	every	DET
ejpam-393	665	11	isomorphism	isomorphism	NOUN
ejpam-393	665	12	between	between	ADP
ejpam-393	665	13	finitely	finitely	ADV
ejpam-393	665	14	generated	generate	VERB
ejpam-393	665	15	substructures	substructure	NOUN
ejpam-393	665	16	extends	extend	VERB
ejpam-393	665	17	to	to	ADP
ejpam-393	665	18	an	an	DET
ejpam-393	665	19	automorphism	automorphism	NOUN
ejpam-393	665	20	of	of	ADP
ejpam-393	665	21	d.	d.	PROPN
ejpam-393	665	22	note	note	VERB
ejpam-393	665	23	that	that	SCONJ
ejpam-393	665	24	if	if	SCONJ
ejpam-393	665	25	d	d	NOUN
ejpam-393	665	26	is	be	AUX
ejpam-393	665	27	homogeneous	homogeneous	ADJ
ejpam-393	665	28	,	,	PUNCT
ejpam-393	665	29	then	then	ADV
ejpam-393	665	30	it	it	PRON
ejpam-393	665	31	is	be	AUX
ejpam-393	665	32	weakly	weakly	ADV
ejpam-393	665	33	homogeneous	homogeneous	ADJ
ejpam-393	665	34	.	.	PUNCT
ejpam-393	666	1	we	we	PRON
ejpam-393	666	2	recall	recall	VERB
ejpam-393	666	3	from	from	ADP
ejpam-393	666	4	[	[	X
ejpam-393	666	5	6	6	NUM
ejpam-393	666	6	]	]	PUNCT
ejpam-393	666	7	thm	thm	PROPN
ejpam-393	666	8	7.1.2	7.1.2	PROPN
ejpam-393	666	9	,	,	PUNCT
ejpam-393	666	10	a	a	DET
ejpam-393	666	11	theorem	theorem	NOUN
ejpam-393	666	12	of	of	ADP
ejpam-393	666	13	fraisse	fraisse	NOUN
ejpam-393	666	14	that	that	PRON
ejpam-393	666	15	puts	put	VERB
ejpam-393	666	16	the	the	DET
ejpam-393	666	17	above	above	ADJ
ejpam-393	666	18	pieces	piece	NOUN
ejpam-393	666	19	together	together	ADV
ejpam-393	666	20	.	.	PUNCT
ejpam-393	667	1	theorem	theorem	VERB
ejpam-393	667	2	6	6	NUM
ejpam-393	667	3	.	.	PUNCT
ejpam-393	668	1	let	let	VERB
ejpam-393	668	2	l	l	NOUN
ejpam-393	668	3	be	be	AUX
ejpam-393	668	4	a	a	DET
ejpam-393	668	5	countable	countable	ADJ
ejpam-393	668	6	signature	signature	NOUN
ejpam-393	668	7	and	and	CCONJ
ejpam-393	668	8	let	let	VERB
ejpam-393	668	9	k	k	PRON
ejpam-393	668	10	be	be	AUX
ejpam-393	668	11	a	a	DET
ejpam-393	668	12	non	non	ADJ
ejpam-393	668	13	-	-	ADJ
ejpam-393	668	14	empty	empty	ADJ
ejpam-393	668	15	finite	finite	NOUN
ejpam-393	668	16	or	or	CCONJ
ejpam-393	668	17	countable	countable	ADJ
ejpam-393	668	18	set	set	NOUN
ejpam-393	668	19	of	of	ADP
ejpam-393	668	20	finitely	finitely	ADV
ejpam-393	668	21	generated	generate	VERB
ejpam-393	668	22	l	l	NOUN
ejpam-393	668	23	-	-	NOUN
ejpam-393	668	24	structures	structure	NOUN
ejpam-393	668	25	which	which	PRON
ejpam-393	668	26	has	have	AUX
ejpam-393	668	27	hp	hp	PROPN
ejpam-393	668	28	,	,	PUNCT
ejpam-393	668	29	j	j	PROPN
ejpam-393	668	30	ep	ep	PROPN
ejpam-393	668	31	and	and	CCONJ
ejpam-393	668	32	ap	ap	PROPN
ejpam-393	668	33	.	.	PUNCT
ejpam-393	669	1	then	then	ADV
ejpam-393	669	2	there	there	PRON
ejpam-393	669	3	is	be	VERB
ejpam-393	669	4	an	an	DET
ejpam-393	669	5	l	l	NOUN
ejpam-393	669	6	structure	structure	NOUN
ejpam-393	669	7	d	d	NOUN
ejpam-393	669	8	,	,	PUNCT
ejpam-393	669	9	unique	unique	ADJ
ejpam-393	669	10	up	up	ADP
ejpam-393	669	11	to	to	ADP
ejpam-393	669	12	isomorphism	isomorphism	NOUN
ejpam-393	669	13	,	,	PUNCT
ejpam-393	669	14	such	such	ADJ
ejpam-393	669	15	that	that	SCONJ
ejpam-393	669	16	(	(	PUNCT
ejpam-393	669	17	1	1	X
ejpam-393	669	18	)	)	PUNCT
ejpam-393	669	19	d	d	NOUN
ejpam-393	669	20	has	have	AUX
ejpam-393	669	21	cardinality	cardinality	PROPN
ejpam-393	669	22	≤ω	≤ω	PROPN
ejpam-393	669	23	(	(	PUNCT
ejpam-393	669	24	2	2	NUM
ejpam-393	669	25	)	)	PUNCT
ejpam-393	669	26	k	k	X
ejpam-393	669	27	is	be	AUX
ejpam-393	669	28	the	the	DET
ejpam-393	669	29	age	age	NOUN
ejpam-393	669	30	of	of	ADP
ejpam-393	669	31	d	d	PROPN
ejpam-393	669	32	,	,	PUNCT
ejpam-393	669	33	and	and	CCONJ
ejpam-393	669	34	(	(	PUNCT
ejpam-393	669	35	3	3	X
ejpam-393	669	36	)	)	PUNCT
ejpam-393	669	37	d	d	NOUN
ejpam-393	669	38	is	be	AUX
ejpam-393	669	39	homogeneous	homogeneous	ADJ
ejpam-393	669	40	.	.	PUNCT
ejpam-393	670	1	following	follow	VERB
ejpam-393	670	2	hodges	hodge	NOUN
ejpam-393	670	3	[	[	X
ejpam-393	670	4	6	6	NUM
ejpam-393	670	5	]	]	PUNCT
ejpam-393	670	6	we	we	PRON
ejpam-393	670	7	also	also	ADV
ejpam-393	670	8	refer	refer	VERB
ejpam-393	670	9	to	to	ADP
ejpam-393	670	10	d	d	NOUN
ejpam-393	670	11	is	be	AUX
ejpam-393	670	12	as	as	ADP
ejpam-393	670	13	fraisse	fraisse	NOUN
ejpam-393	670	14	limit	limit	NOUN
ejpam-393	670	15	of	of	ADP
ejpam-393	670	16	the	the	DET
ejpam-393	670	17	class	class	NOUN
ejpam-393	670	18	k.	k.	PROPN
ejpam-393	671	1	our	our	PRON
ejpam-393	671	2	next	next	ADJ
ejpam-393	671	3	theorem	theorem	NOUN
ejpam-393	671	4	,	,	PUNCT
ejpam-393	671	5	gives	give	VERB
ejpam-393	671	6	a	a	DET
ejpam-393	671	7	sufficient	sufficient	ADJ
ejpam-393	671	8	condition	condition	NOUN
ejpam-393	671	9	for	for	ADP
ejpam-393	671	10	when	when	SCONJ
ejpam-393	671	11	the	the	DET
ejpam-393	671	12	fraisse	fraisse	NOUN
ejpam-393	671	13	limit	limit	NOUN
ejpam-393	671	14	d	d	X
ejpam-393	671	15	of	of	ADP
ejpam-393	671	16	a	a	DET
ejpam-393	671	17	class	class	NOUN
ejpam-393	671	18	k	k	PROPN
ejpam-393	671	19	of	of	ADP
ejpam-393	671	20	finitely	finitely	ADV
ejpam-393	671	21	generated	generate	VERB
ejpam-393	671	22	structures	structure	NOUN
ejpam-393	671	23	,	,	PUNCT
ejpam-393	671	24	has	have	AUX
ejpam-393	671	25	quantifier	quantifi	ADJ
ejpam-393	671	26	elimination	elimination	NOUN
ejpam-393	671	27	.	.	PUNCT
ejpam-393	672	1	recall	recall	VERB
ejpam-393	672	2	that	that	SCONJ
ejpam-393	672	3	an	an	DET
ejpam-393	672	4	l	l	NOUN
ejpam-393	672	5	-	-	NOUN
ejpam-393	672	6	structure	structure	NOUN
ejpam-393	672	7	m	m	NOUN
ejpam-393	672	8	has	have	VERB
ejpam-393	672	9	quantifier	quantifi	ADJ
ejpam-393	672	10	elimination	elimination	NOUN
ejpam-393	672	11	if	if	SCONJ
ejpam-393	672	12	every	every	DET
ejpam-393	672	13	l	l	NOUN
ejpam-393	672	14	formula	formula	NOUN
ejpam-393	672	15	φ	φ	PROPN
ejpam-393	672	16	(	(	PUNCT
ejpam-393	672	17	x̄	x̄	PROPN
ejpam-393	672	18	)	)	PUNCT
ejpam-393	672	19	is	be	AUX
ejpam-393	672	20	equivalent	equivalent	ADJ
ejpam-393	672	21	in	in	ADP
ejpam-393	672	22	m	m	PROPN
ejpam-393	672	23	to	to	ADP
ejpam-393	672	24	a	a	DET
ejpam-393	672	25	boolean	boolean	ADJ
ejpam-393	672	26	combination	combination	NOUN
ejpam-393	672	27	of	of	ADP
ejpam-393	672	28	quantifier	quantifier	NOUN
ejpam-393	672	29	free	free	ADJ
ejpam-393	672	30	formulas	formula	NOUN
ejpam-393	672	31	,	,	PUNCT
ejpam-393	672	32	equivalently	equivalently	ADV
ejpam-393	672	33	atomic	atomic	ADJ
ejpam-393	672	34	formulas	formula	NOUN
ejpam-393	672	35	.	.	PUNCT
ejpam-393	673	1	a	a	DET
ejpam-393	673	2	theory	theory	NOUN
ejpam-393	673	3	t	t	NOUN
ejpam-393	673	4	is	be	AUX
ejpam-393	673	5	ωcategorical	ωcategorical	ADJ
ejpam-393	673	6	if	if	SCONJ
ejpam-393	673	7	all	all	DET
ejpam-393	673	8	countable	countable	ADJ
ejpam-393	673	9	models	model	NOUN
ejpam-393	673	10	of	of	ADP
ejpam-393	673	11	t	t	PROPN
ejpam-393	673	12	are	be	AUX
ejpam-393	673	13	isomorphic	isomorphic	ADJ
ejpam-393	673	14	.	.	PUNCT
ejpam-393	674	1	lemma	lemma	PROPN
ejpam-393	674	2	8	8	NUM
ejpam-393	674	3	.	.	PUNCT
ejpam-393	674	4	suppose	suppose	VERB
ejpam-393	674	5	that	that	SCONJ
ejpam-393	674	6	the	the	DET
ejpam-393	674	7	signature	signature	NOUN
ejpam-393	674	8	l	l	NOUN
ejpam-393	674	9	is	be	AUX
ejpam-393	674	10	finite	finite	ADJ
ejpam-393	674	11	and	and	CCONJ
ejpam-393	674	12	has	have	VERB
ejpam-393	674	13	no	no	DET
ejpam-393	674	14	function	function	NOUN
ejpam-393	674	15	symbols	symbol	NOUN
ejpam-393	674	16	.	.	PUNCT
ejpam-393	675	1	suppose	suppose	VERB
ejpam-393	675	2	that	that	SCONJ
ejpam-393	675	3	k	k	PROPN
ejpam-393	675	4	is	be	AUX
ejpam-393	675	5	a	a	DET
ejpam-393	675	6	countable	countable	ADJ
ejpam-393	675	7	set	set	NOUN
ejpam-393	675	8	of	of	ADP
ejpam-393	675	9	finite	finite	ADJ
ejpam-393	675	10	l	l	PROPN
ejpam-393	675	11	structures	structure	NOUN
ejpam-393	675	12	with	with	ADP
ejpam-393	675	13	hp	hp	PROPN
ejpam-393	675	14	,	,	PUNCT
ejpam-393	675	15	j	j	PROPN
ejpam-393	675	16	ep	ep	PROPN
ejpam-393	675	17	and	and	CCONJ
ejpam-393	675	18	ap	ap	PROPN
ejpam-393	675	19	.	.	PUNCT
ejpam-393	676	1	let	let	VERB
ejpam-393	676	2	m	m	PRON
ejpam-393	676	3	be	be	AUX
ejpam-393	676	4	the	the	DET
ejpam-393	676	5	fraisse	fraisse	ADJ
ejpam-393	676	6	limit	limit	NOUN
ejpam-393	676	7	of	of	ADP
ejpam-393	676	8	k.	k.	PROPN
ejpam-393	676	9	let	let	VERB
ejpam-393	676	10	t	t	PROPN
ejpam-393	676	11	be	be	AUX
ejpam-393	676	12	the	the	DET
ejpam-393	676	13	first	first	ADJ
ejpam-393	676	14	order	order	NOUN
ejpam-393	676	15	theory	theory	NOUN
ejpam-393	676	16	th(m	th(m	NOUN
ejpam-393	676	17	)	)	PUNCT
ejpam-393	676	18	of	of	ADP
ejpam-393	676	19	m.	m.	NOUN
ejpam-393	676	20	then	then	ADV
ejpam-393	676	21	(	(	PUNCT
ejpam-393	676	22	i	i	NOUN
ejpam-393	676	23	)	)	PUNCT
ejpam-393	676	24	t	t	PROPN
ejpam-393	676	25	is	be	AUX
ejpam-393	676	26	ω	ω	NOUN
ejpam-393	676	27	-	-	ADJ
ejpam-393	676	28	categorial	categorial	ADJ
ejpam-393	676	29	.	.	PUNCT
ejpam-393	677	1	(	(	PUNCT
ejpam-393	677	2	ii	ii	X
ejpam-393	677	3	)	)	PUNCT
ejpam-393	677	4	m	m	AUX
ejpam-393	677	5	has	have	VERB
ejpam-393	677	6	quantifier	quantifier	NOUN
ejpam-393	677	7	elimination	elimination	NOUN
ejpam-393	677	8	proof	proof	NOUN
ejpam-393	677	9	.	.	PUNCT
ejpam-393	678	1	the	the	DET
ejpam-393	678	2	proof	proof	NOUN
ejpam-393	678	3	is	be	AUX
ejpam-393	678	4	taken	take	VERB
ejpam-393	678	5	from	from	ADP
ejpam-393	678	6	[	[	X
ejpam-393	678	7	6	6	NUM
ejpam-393	678	8	]	]	PUNCT
ejpam-393	678	9	.	.	PUNCT
ejpam-393	679	1	we	we	PRON
ejpam-393	679	2	include	include	VERB
ejpam-393	679	3	it	it	PRON
ejpam-393	679	4	for	for	ADP
ejpam-393	679	5	the	the	DET
ejpam-393	679	6	sake	sake	NOUN
ejpam-393	679	7	of	of	ADP
ejpam-393	679	8	completeness	completeness	NOUN
ejpam-393	679	9	.	.	PUNCT
ejpam-393	680	1	we	we	PRON
ejpam-393	680	2	note	note	VERB
ejpam-393	680	3	that	that	SCONJ
ejpam-393	680	4	the	the	DET
ejpam-393	680	5	following	follow	VERB
ejpam-393	680	6	hold	hold	NOUN
ejpam-393	680	7	:	:	PUNCT
ejpam-393	680	8	if	if	SCONJ
ejpam-393	680	9	a	a	PRON
ejpam-393	680	10	is	be	AUX
ejpam-393	680	11	any	any	DET
ejpam-393	680	12	finite	finite	ADJ
ejpam-393	680	13	l	l	NOUN
ejpam-393	680	14	structure	structure	NOUN
ejpam-393	680	15	with	with	ADP
ejpam-393	680	16	n	n	PROPN
ejpam-393	680	17	generators	generator	NOUN
ejpam-393	680	18	ā	ā	VERB
ejpam-393	680	19	,	,	PUNCT
ejpam-393	680	20	then	then	ADV
ejpam-393	680	21	there	there	PRON
ejpam-393	680	22	is	be	VERB
ejpam-393	680	23	a	a	DET
ejpam-393	680	24	quantifier	quantifier	NOUN
ejpam-393	680	25	free	free	ADJ
ejpam-393	680	26	formula	formula	NOUN
ejpam-393	680	27	ψa	ψa	ADP
ejpam-393	680	28	,	,	PUNCT
ejpam-393	680	29	ā(x0	ā(x0	NOUN
ejpam-393	680	30	.	.	PUNCT
ejpam-393	680	31	.	.	PUNCT
ejpam-393	680	32	.	.	PUNCT
ejpam-393	681	1	xn−1	xn−1	PROPN
ejpam-393	681	2	)	)	PUNCT
ejpam-393	681	3	such	such	ADJ
ejpam-393	681	4	that	that	PRON
ejpam-393	681	5	for	for	ADP
ejpam-393	681	6	any	any	DET
ejpam-393	681	7	l	l	NOUN
ejpam-393	681	8	structure	structure	NOUN
ejpam-393	681	9	b	b	PROPN
ejpam-393	681	10	and	and	CCONJ
ejpam-393	681	11	n	n	CCONJ
ejpam-393	681	12	-	-	PUNCT
ejpam-393	681	13	tuple	tuple	ADJ
ejpam-393	681	14	b̄	b̄	NOUN
ejpam-393	681	15	of	of	ADP
ejpam-393	681	16	elements	element	NOUN
ejpam-393	681	17	of	of	ADP
ejpam-393	681	18	b	b	NOUN
ejpam-393	681	19	,	,	PUNCT
ejpam-393	681	20	(	(	PUNCT
ejpam-393	681	21	1	1	X
ejpam-393	681	22	)	)	PUNCT
ejpam-393	681	23	b	b	NOUN
ejpam-393	681	24	|=	|=	X
ejpam-393	681	25	φ	φ	NOUN
ejpam-393	681	26	[	[	PUNCT
ejpam-393	681	27	b̄	b̄	NOUN
ejpam-393	681	28	]	]	PUNCT
ejpam-393	681	29	if	if	SCONJ
ejpam-393	681	30	and	and	CCONJ
ejpam-393	681	31	only	only	ADV
ejpam-393	681	32	if	if	SCONJ
ejpam-393	681	33	there	there	PRON
ejpam-393	681	34	is	be	VERB
ejpam-393	681	35	an	an	DET
ejpam-393	681	36	isomorphism	isomorphism	NOUN
ejpam-393	681	37	from	from	ADP
ejpam-393	681	38	a	a	PRON
ejpam-393	681	39	to	to	ADP
ejpam-393	681	40	〈	〈	NOUN
ejpam-393	681	41	b〉b	b〉b	PROPN
ejpam-393	681	42	which	which	PRON
ejpam-393	681	43	takes	take	VERB
ejpam-393	681	44	ā	ā	NOUN
ejpam-393	681	45	to	to	ADP
ejpam-393	681	46	b̄.	b̄.	PUNCT
ejpam-393	681	47	in	in	ADP
ejpam-393	681	48	fact	fact	NOUN
ejpam-393	681	49	ψa	ψa	ADP
ejpam-393	681	50	,	,	PUNCT
ejpam-393	681	51	ā	ā	PROPN
ejpam-393	681	52	is	be	AUX
ejpam-393	681	53	a	a	DET
ejpam-393	681	54	conjunction	conjunction	NOUN
ejpam-393	681	55	of	of	ADP
ejpam-393	681	56	literals	literal	NOUN
ejpam-393	681	57	satisfied	satisfy	VERB
ejpam-393	681	58	by	by	ADP
ejpam-393	681	59	ā	ā	PROPN
ejpam-393	681	60	in	in	ADP
ejpam-393	681	61	a.	a.	NOUN
ejpam-393	681	62	also	also	ADV
ejpam-393	681	63	or	or	CCONJ
ejpam-393	681	64	each	each	DET
ejpam-393	681	65	n	n	CCONJ
ejpam-393	681	66	<	<	X
ejpam-393	681	67	ω	ω	X
ejpam-393	681	68	there	there	PRON
ejpam-393	681	69	are	be	VERB
ejpam-393	681	70	only	only	ADV
ejpam-393	681	71	finitely	finitely	ADV
ejpam-393	681	72	many	many	ADJ
ejpam-393	681	73	isomorphism	isomorphism	NOUN
ejpam-393	681	74	types	type	NOUN
ejpam-393	681	75	of	of	ADP
ejpam-393	681	76	structures	structure	NOUN
ejpam-393	681	77	in	in	ADP
ejpam-393	681	78	k	k	PROPN
ejpam-393	681	79	with	with	ADP
ejpam-393	681	80	n	n	PRON
ejpam-393	681	81	generators	generator	NOUN
ejpam-393	681	82	.	.	PUNCT
ejpam-393	682	1	let	let	VERB
ejpam-393	682	2	u0	u0	ADJ
ejpam-393	682	3	be	be	AUX
ejpam-393	682	4	the	the	DET
ejpam-393	682	5	set	set	NOUN
ejpam-393	682	6	of	of	ADP
ejpam-393	682	7	all	all	DET
ejpam-393	682	8	sentences	sentence	NOUN
ejpam-393	682	9	of	of	ADP
ejpam-393	682	10	the	the	DET
ejpam-393	682	11	form	form	NOUN
ejpam-393	682	12	(	(	PUNCT
ejpam-393	682	13	∀	∀	X
ejpam-393	682	14	x̄)(ψa	x̄)(ψa	X
ejpam-393	682	15	,	,	PUNCT
ejpam-393	682	16	ā	ā	NOUN
ejpam-393	682	17	(	(	PUNCT
ejpam-393	682	18	x̄	x̄	NOUN
ejpam-393	682	19	)	)	PUNCT
ejpam-393	683	1	=	=	VERB
ejpam-393	683	2	⇒	⇒	NOUN
ejpam-393	683	3	∃yψb	∃yψb	ADJ
ejpam-393	683	4	,	,	PUNCT
ejpam-393	683	5	āb	āb	PROPN
ejpam-393	683	6	(	(	PUNCT
ejpam-393	683	7	x̄	x̄	NOUN
ejpam-393	683	8	,	,	PUNCT
ejpam-393	683	9	y	y	PROPN
ejpam-393	683	10	)	)	PUNCT
ejpam-393	683	11	)	)	PUNCT
ejpam-393	683	12	(	(	PUNCT
ejpam-393	683	13	4	4	X
ejpam-393	683	14	)	)	PUNCT
ejpam-393	683	15	t.	t.	NOUN
ejpam-393	683	16	ahmed	ahmed	PROPN
ejpam-393	683	17	/	/	SYM
ejpam-393	683	18	eur	eur	PROPN
ejpam-393	683	19	.	.	PUNCT
ejpam-393	684	1	j.	j.	PROPN
ejpam-393	684	2	pure	pure	PROPN
ejpam-393	684	3	appl	appl	PROPN
ejpam-393	684	4	.	.	PROPN
ejpam-393	684	5	math	math	PROPN
ejpam-393	684	6	,	,	PUNCT
ejpam-393	684	7	3	3	NUM
ejpam-393	684	8	(	(	PUNCT
ejpam-393	684	9	2010	2010	NUM
ejpam-393	684	10	)	)	PUNCT
ejpam-393	684	11	,	,	PUNCT
ejpam-393	684	12	853	853	NUM
ejpam-393	684	13	-	-	SYM
ejpam-393	684	14	880	880	NUM
ejpam-393	684	15	869	869	NUM
ejpam-393	684	16	where	where	SCONJ
ejpam-393	684	17	b	b	NOUN
ejpam-393	684	18	is	be	AUX
ejpam-393	684	19	a	a	DET
ejpam-393	684	20	structure	structure	NOUN
ejpam-393	684	21	in	in	ADP
ejpam-393	684	22	k	k	PROPN
ejpam-393	684	23	generated	generate	VERB
ejpam-393	684	24	by	by	ADP
ejpam-393	684	25	a	a	DET
ejpam-393	684	26	tuple	tuple	PROPN
ejpam-393	684	27	ā	ā	PROPN
ejpam-393	684	28	b	b	PROPN
ejpam-393	684	29	of	of	ADP
ejpam-393	684	30	distinct	distinct	ADJ
ejpam-393	684	31	elements	element	NOUN
ejpam-393	684	32	,	,	PUNCT
ejpam-393	684	33	and	and	CCONJ
ejpam-393	684	34	a	a	PRON
ejpam-393	684	35	is	be	AUX
ejpam-393	684	36	the	the	DET
ejpam-393	684	37	substructure	substructure	NOUN
ejpam-393	684	38	generated	generate	VERB
ejpam-393	684	39	by	by	ADP
ejpam-393	684	40	ā.	ā.	NOUN
ejpam-393	684	41	let	let	VERB
ejpam-393	684	42	u1	u1	NOUN
ejpam-393	684	43	be	be	AUX
ejpam-393	684	44	the	the	DET
ejpam-393	684	45	set	set	NOUN
ejpam-393	684	46	of	of	ADP
ejpam-393	684	47	sentences	sentence	NOUN
ejpam-393	684	48	of	of	ADP
ejpam-393	684	49	the	the	DET
ejpam-393	684	50	form	form	NOUN
ejpam-393	684	51	(	(	PUNCT
ejpam-393	684	52	∀x	∀x	X
ejpam-393	684	53	)	)	PUNCT
ejpam-393	684	54	∨	∨	NUM
ejpam-393	684	55	ψa	ψa	PROPN
ejpam-393	684	56	,	,	PUNCT
ejpam-393	684	57	ā	ā	PROPN
ejpam-393	684	58	(	(	PUNCT
ejpam-393	684	59	x̄	x̄	PROPN
ejpam-393	684	60	)	)	PUNCT
ejpam-393	684	61	(	(	PUNCT
ejpam-393	684	62	5	5	X
ejpam-393	684	63	)	)	PUNCT
ejpam-393	684	64	where	where	SCONJ
ejpam-393	684	65	the	the	DET
ejpam-393	684	66	disjunction	disjunction	NOUN
ejpam-393	684	67	is	be	AUX
ejpam-393	684	68	over	over	ADP
ejpam-393	684	69	all	all	DET
ejpam-393	684	70	pairs	pair	NOUN
ejpam-393	684	71	a	a	PRON
ejpam-393	684	72	,	,	PUNCT
ejpam-393	684	73	ā	ā	NOUN
ejpam-393	684	74	such	such	ADJ
ejpam-393	684	75	that	that	SCONJ
ejpam-393	684	76	a	a	DET
ejpam-393	684	77	∈	∈	PROPN
ejpam-393	684	78	k	k	NOUN
ejpam-393	684	79	and	and	CCONJ
ejpam-393	684	80	ā	ā	PROPN
ejpam-393	684	81	is	be	AUX
ejpam-393	684	82	a	a	DET
ejpam-393	684	83	tuple	tuple	NOUN
ejpam-393	684	84	of	of	ADP
ejpam-393	684	85	the	the	DET
ejpam-393	684	86	same	same	ADJ
ejpam-393	684	87	length	length	NOUN
ejpam-393	684	88	as	as	ADP
ejpam-393	684	89	x̄	x̄	PRON
ejpam-393	684	90	which	which	PRON
ejpam-393	684	91	generates	generate	VERB
ejpam-393	684	92	a.	a.	NOUN
ejpam-393	685	1	then	then	ADV
ejpam-393	685	2	this	this	PRON
ejpam-393	685	3	is	be	AUX
ejpam-393	685	4	a	a	DET
ejpam-393	685	5	finite	finite	ADJ
ejpam-393	685	6	disjunction	disjunction	NOUN
ejpam-393	685	7	.	.	PUNCT
ejpam-393	686	1	let	let	VERB
ejpam-393	686	2	u	u	PRON
ejpam-393	686	3	=	=	NOUN
ejpam-393	686	4	u0	u0	ADJ
ejpam-393	686	5	∪u1	∪u1	PROPN
ejpam-393	686	6	.	.	PUNCT
ejpam-393	687	1	then	then	ADV
ejpam-393	687	2	m	m	VERB
ejpam-393	687	3	is	be	AUX
ejpam-393	687	4	a	a	DET
ejpam-393	687	5	model	model	NOUN
ejpam-393	687	6	of	of	ADP
ejpam-393	687	7	u	u	PROPN
ejpam-393	687	8	.	.	PUNCT
ejpam-393	688	1	suppose	suppose	VERB
ejpam-393	688	2	that	that	SCONJ
ejpam-393	688	3	d	d	PROPN
ejpam-393	688	4	is	be	AUX
ejpam-393	688	5	any	any	DET
ejpam-393	688	6	countable	countable	ADJ
ejpam-393	688	7	model	model	NOUN
ejpam-393	688	8	of	of	ADP
ejpam-393	688	9	u	u	PROPN
ejpam-393	688	10	.	.	PUNCT
ejpam-393	689	1	then	then	ADV
ejpam-393	689	2	the	the	DET
ejpam-393	689	3	sentences	sentence	NOUN
ejpam-393	689	4	(	(	PUNCT
ejpam-393	689	5	1	1	X
ejpam-393	689	6	)	)	PUNCT
ejpam-393	689	7	say	say	VERB
ejpam-393	689	8	that	that	SCONJ
ejpam-393	689	9	if	if	SCONJ
ejpam-393	689	10	(	(	PUNCT
ejpam-393	689	11	4	4	X
ejpam-393	689	12	)	)	PUNCT
ejpam-393	689	13	a	a	PRON
ejpam-393	689	14	,	,	PUNCT
ejpam-393	689	15	b	b	NOUN
ejpam-393	689	16	are	be	AUX
ejpam-393	689	17	finitely	finitely	ADV
ejpam-393	689	18	generated	generate	VERB
ejpam-393	689	19	substructures	substructure	NOUN
ejpam-393	689	20	of	of	ADP
ejpam-393	689	21	d	d	PROPN
ejpam-393	689	22	a⊆	a⊆	PROPN
ejpam-393	689	23	b	b	PROPN
ejpam-393	689	24	,	,	PUNCT
ejpam-393	689	25	b	b	PROPN
ejpam-393	689	26	comes	come	VERB
ejpam-393	689	27	from	from	ADP
ejpam-393	689	28	a	a	PRON
ejpam-393	689	29	by	by	ADP
ejpam-393	689	30	adding	add	VERB
ejpam-393	689	31	one	one	NUM
ejpam-393	689	32	more	more	ADJ
ejpam-393	689	33	generator	generator	NOUN
ejpam-393	689	34	,	,	PUNCT
ejpam-393	689	35	and	and	CCONJ
ejpam-393	689	36	f	f	X
ejpam-393	689	37	:	:	PUNCT
ejpam-393	689	38	a	a	PRON
ejpam-393	689	39	→	→	SYM
ejpam-393	689	40	d	d	NOUN
ejpam-393	689	41	is	be	AUX
ejpam-393	689	42	an	an	DET
ejpam-393	689	43	embedding	embedding	NOUN
ejpam-393	689	44	,	,	PUNCT
ejpam-393	689	45	then	then	ADV
ejpam-393	689	46	there	there	PRON
ejpam-393	689	47	is	be	VERB
ejpam-393	689	48	an	an	DET
ejpam-393	689	49	embedding	embed	VERB
ejpam-393	689	50	g	g	NOUN
ejpam-393	689	51	:	:	PUNCT
ejpam-393	689	52	b	b	X
ejpam-393	689	53	→	→	SYM
ejpam-393	689	54	d	d	X
ejpam-393	689	55	which	which	PRON
ejpam-393	689	56	extends	extend	VERB
ejpam-393	689	57	f	f	PROPN
ejpam-393	689	58	.	.	PUNCT
ejpam-393	690	1	using	use	VERB
ejpam-393	690	2	induction	induction	NOUN
ejpam-393	690	3	on	on	ADP
ejpam-393	690	4	the	the	DET
ejpam-393	690	5	number	number	NOUN
ejpam-393	690	6	of	of	ADP
ejpam-393	690	7	generators	generator	NOUN
ejpam-393	690	8	,	,	PUNCT
ejpam-393	690	9	imply	imply	VERB
ejpam-393	690	10	that	that	SCONJ
ejpam-393	690	11	every	every	DET
ejpam-393	690	12	structure	structure	NOUN
ejpam-393	690	13	in	in	ADP
ejpam-393	690	14	k	k	PROPN
ejpam-393	690	15	is	be	AUX
ejpam-393	690	16	embeddable	embeddable	ADJ
ejpam-393	690	17	in	in	ADP
ejpam-393	690	18	d	d	PROPN
ejpam-393	690	19	;	;	PUNCT
ejpam-393	690	20	so	so	ADV
ejpam-393	690	21	together	together	ADV
ejpam-393	690	22	with	with	ADP
ejpam-393	690	23	(	(	PUNCT
ejpam-393	690	24	3	3	X
ejpam-393	690	25	)	)	PUNCT
ejpam-393	690	26	this	this	PRON
ejpam-393	690	27	implies	imply	VERB
ejpam-393	690	28	that	that	SCONJ
ejpam-393	690	29	the	the	DET
ejpam-393	690	30	age	age	NOUN
ejpam-393	690	31	of	of	ADP
ejpam-393	690	32	d	d	PROPN
ejpam-393	690	33	is	be	AUX
ejpam-393	690	34	exactly	exactly	ADV
ejpam-393	690	35	k.	k.	ADV
ejpam-393	690	36	using	use	VERB
ejpam-393	690	37	(	(	PUNCT
ejpam-393	690	38	2	2	NUM
ejpam-393	690	39	)	)	PUNCT
ejpam-393	690	40	an	an	DET
ejpam-393	690	41	induction	induction	NOUN
ejpam-393	690	42	on	on	ADP
ejpam-393	690	43	the	the	DET
ejpam-393	690	44	size	size	NOUN
ejpam-393	690	45	of	of	ADP
ejpam-393	690	46	dom(b	dom(b	PROPN
ejpam-393	690	47	)	)	PUNCT
ejpam-393	690	48	\	\	NOUN
ejpam-393	690	49	dom(a	dom(a	PROPN
ejpam-393	690	50	)	)	PUNCT
ejpam-393	690	51	,	,	PUNCT
ejpam-393	690	52	tells	tell	VERB
ejpam-393	690	53	us	we	PRON
ejpam-393	690	54	that	that	SCONJ
ejpam-393	690	55	d	d	PRON
ejpam-393	690	56	is	be	AUX
ejpam-393	690	57	weakly	weakly	ADV
ejpam-393	690	58	homogeneous	homogeneous	ADJ
ejpam-393	690	59	,	,	PUNCT
ejpam-393	690	60	so	so	CCONJ
ejpam-393	690	61	d	d	NOUN
ejpam-393	690	62	is	be	AUX
ejpam-393	690	63	isomorphic	isomorphic	ADJ
ejpam-393	690	64	to	to	AUX
ejpam-393	690	65	m.	m.	NOUN
ejpam-393	690	66	hence	hence	ADV
ejpam-393	690	67	u	u	PROPN
ejpam-393	690	68	is	be	AUX
ejpam-393	690	69	ω	ω	NUM
ejpam-393	690	70	categorical	categorical	ADJ
ejpam-393	690	71	and	and	CCONJ
ejpam-393	690	72	u	u	NOUN
ejpam-393	690	73	is	be	AUX
ejpam-393	690	74	a	a	DET
ejpam-393	690	75	set	set	NOUN
ejpam-393	690	76	of	of	ADP
ejpam-393	690	77	axioms	axiom	NOUN
ejpam-393	690	78	for	for	ADP
ejpam-393	690	79	t	t	PROPN
ejpam-393	690	80	.	.	PUNCT
ejpam-393	691	1	suppose	suppose	VERB
ejpam-393	691	2	now	now	ADV
ejpam-393	691	3	that	that	SCONJ
ejpam-393	691	4	φ	φ	PROPN
ejpam-393	691	5	(	(	PUNCT
ejpam-393	691	6	x̄	x̄	PROPN
ejpam-393	691	7	)	)	PUNCT
ejpam-393	691	8	is	be	AUX
ejpam-393	691	9	a	a	DET
ejpam-393	691	10	formula	formula	NOUN
ejpam-393	691	11	of	of	ADP
ejpam-393	691	12	l	l	NOUN
ejpam-393	691	13	,	,	PUNCT
ejpam-393	691	14	and	and	CCONJ
ejpam-393	691	15	let	let	VERB
ejpam-393	691	16	x	x	PRON
ejpam-393	691	17	be	be	AUX
ejpam-393	691	18	the	the	DET
ejpam-393	691	19	set	set	NOUN
ejpam-393	691	20	of	of	ADP
ejpam-393	691	21	all	all	DET
ejpam-393	691	22	tuples	tuple	NOUN
ejpam-393	691	23	ā	ā	ADJ
ejpam-393	691	24	in	in	ADP
ejpam-393	691	25	m	m	PRON
ejpam-393	691	26	such	such	ADJ
ejpam-393	691	27	that	that	SCONJ
ejpam-393	691	28	m	m	VERB
ejpam-393	691	29	|=	|=	NOUN
ejpam-393	691	30	φ(ā	φ(ā	NUM
ejpam-393	691	31	)	)	PUNCT
ejpam-393	691	32	.	.	PUNCT
ejpam-393	692	1	if	if	SCONJ
ejpam-393	692	2	ā	ā	NOUN
ejpam-393	692	3	is	be	AUX
ejpam-393	692	4	in	in	ADP
ejpam-393	692	5	x	x	X
ejpam-393	692	6	,	,	PUNCT
ejpam-393	692	7	and	and	CCONJ
ejpam-393	692	8	b̄	b̄	PROPN
ejpam-393	692	9	is	be	AUX
ejpam-393	692	10	a	a	DET
ejpam-393	692	11	tuple	tuple	NOUN
ejpam-393	692	12	of	of	ADP
ejpam-393	692	13	elements	element	NOUN
ejpam-393	692	14	such	such	ADJ
ejpam-393	692	15	that	that	SCONJ
ejpam-393	692	16	there	there	PRON
ejpam-393	692	17	is	be	VERB
ejpam-393	692	18	an	an	DET
ejpam-393	692	19	isomorphism	isomorphism	NOUN
ejpam-393	692	20	e	e	NOUN
ejpam-393	692	21	:	:	PUNCT
ejpam-393	692	22	〈	〈	PROPN
ejpam-393	692	23	ām	ām	ADJ
ejpam-393	692	24	〉	〉	NOUN
ejpam-393	692	25	→	→	PUNCT
ejpam-393	692	26	〈	〈	ADJ
ejpam-393	692	27	b̄m	b̄m	NOUN
ejpam-393	692	28	〉	〉	NOUN
ejpam-393	692	29	taking	take	VERB
ejpam-393	692	30	ā→	ā→	PROPN
ejpam-393	692	31	b̄	b̄	PROPN
ejpam-393	692	32	,	,	PUNCT
ejpam-393	692	33	then	then	ADV
ejpam-393	692	34	e	e	PROPN
ejpam-393	692	35	extends	extend	VERB
ejpam-393	692	36	to	to	ADP
ejpam-393	692	37	an	an	DET
ejpam-393	692	38	automorphism	automorphism	NOUN
ejpam-393	692	39	of	of	ADP
ejpam-393	692	40	m	m	PROPN
ejpam-393	692	41	,	,	PUNCT
ejpam-393	692	42	so	so	SCONJ
ejpam-393	692	43	that	that	SCONJ
ejpam-393	692	44	b̄	b̄	NOUN
ejpam-393	692	45	is	be	AUX
ejpam-393	692	46	in	in	ADP
ejpam-393	692	47	x	x	PUNCT
ejpam-393	692	48	too	too	ADV
ejpam-393	692	49	.	.	PUNCT
ejpam-393	693	1	it	it	PRON
ejpam-393	693	2	follows	follow	VERB
ejpam-393	693	3	that	that	SCONJ
ejpam-393	693	4	φ	φ	PROPN
ejpam-393	693	5	is	be	AUX
ejpam-393	693	6	equivalent	equivalent	ADJ
ejpam-393	693	7	modulo	modulo	NOUN
ejpam-393	693	8	t	t	NOUN
ejpam-393	693	9	to	to	ADP
ejpam-393	693	10	the	the	DET
ejpam-393	693	11	disjunction	disjunction	NOUN
ejpam-393	693	12	of	of	ADP
ejpam-393	693	13	all	all	DET
ejpam-393	693	14	the	the	DET
ejpam-393	693	15	formulas	formula	NOUN
ejpam-393	693	16	ψ〈ā〉,ā	ψ〈ā〉,ā	PROPN
ejpam-393	693	17	(	(	PUNCT
ejpam-393	693	18	x̄	x̄	PROPN
ejpam-393	693	19	)	)	PUNCT
ejpam-393	693	20	with	with	ADP
ejpam-393	693	21	ā	ā	ADJ
ejpam-393	693	22	∈	∈	PROPN
ejpam-393	693	23	x	x	X
ejpam-393	693	24	.this	.this	PRON
ejpam-393	693	25	is	be	AUX
ejpam-393	693	26	a	a	DET
ejpam-393	693	27	finite	finite	ADJ
ejpam-393	693	28	disjunction	disjunction	NOUN
ejpam-393	693	29	of	of	ADP
ejpam-393	693	30	quantifier	quantifier	NOUN
ejpam-393	693	31	free	free	ADJ
ejpam-393	693	32	formulas	formula	NOUN
ejpam-393	693	33	.	.	PUNCT
ejpam-393	694	1	finally	finally	ADV
ejpam-393	694	2	if	if	SCONJ
ejpam-393	694	3	φ	φ	PROPN
ejpam-393	694	4	is	be	AUX
ejpam-393	694	5	a	a	DET
ejpam-393	694	6	sentence	sentence	NOUN
ejpam-393	694	7	of	of	ADP
ejpam-393	694	8	l	l	NOUN
ejpam-393	694	9	then	then	ADV
ejpam-393	694	10	since	since	SCONJ
ejpam-393	694	11	t	t	PROPN
ejpam-393	694	12	is	be	AUX
ejpam-393	694	13	complete	complete	ADJ
ejpam-393	694	14	,	,	PUNCT
ejpam-393	694	15	φ	φ	PROPN
ejpam-393	694	16	is	be	AUX
ejpam-393	694	17	equivalent	equivalent	ADJ
ejpam-393	694	18	to	to	ADP
ejpam-393	694	19	either	either	CCONJ
ejpam-393	694	20	⊤	⊤	NOUN
ejpam-393	694	21	or	or	CCONJ
ejpam-393	694	22	⊥.	⊥.	NUM
ejpam-393	694	23	notation	notation	NOUN
ejpam-393	694	24	.	.	PUNCT
ejpam-393	695	1	s3	s3	PROPN
ejpam-393	695	2	denotes	denote	VERB
ejpam-393	695	3	the	the	DET
ejpam-393	695	4	set	set	NOUN
ejpam-393	695	5	of	of	ADP
ejpam-393	695	6	all	all	DET
ejpam-393	695	7	permutations	permutation	NOUN
ejpam-393	695	8	of	of	ADP
ejpam-393	695	9	3	3	NUM
ejpam-393	695	10	.	.	PUNCT
ejpam-393	695	11	x	x	SYM
ejpam-393	696	1	y	y	PROPN
ejpam-393	696	2	denotes	denote	VERB
ejpam-393	696	3	the	the	DET
ejpam-393	696	4	set	set	NOUN
ejpam-393	696	5	of	of	ADP
ejpam-393	696	6	functions	function	NOUN
ejpam-393	696	7	from	from	ADP
ejpam-393	696	8	x	x	PUNCT
ejpam-393	696	9	to	to	ADP
ejpam-393	696	10	y	y	PROPN
ejpam-393	696	11	.	.	PUNCT
ejpam-393	697	1	for	for	ADP
ejpam-393	697	2	u	u	NOUN
ejpam-393	697	3	,	,	PUNCT
ejpam-393	697	4	v	v	PROPN
ejpam-393	697	5	∈	∈	PROPN
ejpam-393	697	6	33	33	NUM
ejpam-393	697	7	,	,	PUNCT
ejpam-393	697	8	i	i	PRON
ejpam-393	697	9	<	<	X
ejpam-393	697	10	3	3	NUM
ejpam-393	697	11	we	we	PRON
ejpam-393	697	12	write	write	VERB
ejpam-393	697	13	ui	ui	NOUN
ejpam-393	697	14	for	for	ADP
ejpam-393	697	15	u(i	u(i	NOUN
ejpam-393	697	16	)	)	PUNCT
ejpam-393	697	17	<	<	X
ejpam-393	697	18	3	3	NUM
ejpam-393	697	19	,	,	PUNCT
ejpam-393	697	20	and	and	CCONJ
ejpam-393	697	21	we	we	PRON
ejpam-393	697	22	write	write	VERB
ejpam-393	697	23	u≡i	u≡i	PROPN
ejpam-393	697	24	v	v	ADP
ejpam-393	697	25	if	if	SCONJ
ejpam-393	697	26	u	u	PROPN
ejpam-393	697	27	and	and	CCONJ
ejpam-393	697	28	v	v	NOUN
ejpam-393	697	29	agree	agree	VERB
ejpam-393	697	30	off	off	ADP
ejpam-393	697	31	i	i	PRON
ejpam-393	697	32	,	,	PUNCT
ejpam-393	697	33	i.e	i.e	X
ejpam-393	697	34	if	if	SCONJ
ejpam-393	697	35	u	u	PROPN
ejpam-393	697	36	j	j	PROPN
ejpam-393	697	37	=	=	X
ejpam-393	697	38	v	v	PROPN
ejpam-393	697	39	j	j	PROPN
ejpam-393	697	40	for	for	ADP
ejpam-393	697	41	all	all	DET
ejpam-393	697	42	j	j	PROPN
ejpam-393	697	43	∈	∈	PROPN
ejpam-393	697	44	3r	3r	NOUN
ejpam-393	697	45	{	{	PUNCT
ejpam-393	697	46	i	i	NOUN
ejpam-393	697	47	}	}	PUNCT
ejpam-393	697	48	.	.	PUNCT
ejpam-393	698	1	for	for	ADP
ejpam-393	698	2	a	a	DET
ejpam-393	698	3	symbol	symbol	NOUN
ejpam-393	698	4	r	r	NOUN
ejpam-393	698	5	of	of	ADP
ejpam-393	698	6	the	the	DET
ejpam-393	698	7	signature	signature	NOUN
ejpam-393	698	8	of	of	ADP
ejpam-393	698	9	m	m	VERB
ejpam-393	698	10	we	we	PRON
ejpam-393	698	11	write	write	VERB
ejpam-393	698	12	rm	rm	PROPN
ejpam-393	698	13	for	for	ADP
ejpam-393	698	14	the	the	DET
ejpam-393	698	15	interpretation	interpretation	NOUN
ejpam-393	698	16	of	of	ADP
ejpam-393	698	17	r	r	NOUN
ejpam-393	698	18	in	in	ADP
ejpam-393	698	19	m.	m.	NOUN
ejpam-393	698	20	lemma	lemma	PROPN
ejpam-393	698	21	9	9	X
ejpam-393	698	22	.	.	PUNCT
ejpam-393	699	1	let	let	VERB
ejpam-393	699	2	l	l	NOUN
ejpam-393	699	3	be	be	AUX
ejpam-393	699	4	a	a	DET
ejpam-393	699	5	signature	signature	NOUN
ejpam-393	699	6	consisting	consist	VERB
ejpam-393	699	7	of	of	ADP
ejpam-393	699	8	the	the	DET
ejpam-393	699	9	unary	unary	ADJ
ejpam-393	699	10	relation	relation	NOUN
ejpam-393	699	11	symbols	symbol	NOUN
ejpam-393	699	12	p0	p0	NOUN
ejpam-393	699	13	,	,	PUNCT
ejpam-393	699	14	p1	p1	NOUN
ejpam-393	699	15	,	,	PUNCT
ejpam-393	699	16	p2	p2	PROPN
ejpam-393	699	17	and	and	CCONJ
ejpam-393	699	18	uncountably	uncountably	ADV
ejpam-393	699	19	many	many	ADJ
ejpam-393	699	20	3	3	NUM
ejpam-393	699	21	-	-	PUNCT
ejpam-393	699	22	ary	ary	NOUN
ejpam-393	699	23	predicate	predicate	NOUN
ejpam-393	699	24	symbols	symbol	NOUN
ejpam-393	699	25	.	.	PUNCT
ejpam-393	700	1	for	for	ADP
ejpam-393	700	2	u	u	PROPN
ejpam-393	700	3	∈	∈	PROPN
ejpam-393	700	4	33	33	NUM
ejpam-393	700	5	,	,	PUNCT
ejpam-393	700	6	let	let	VERB
ejpam-393	700	7	χu	χu	PART
ejpam-393	700	8	be	be	AUX
ejpam-393	700	9	the	the	DET
ejpam-393	700	10	formula	formula	NOUN
ejpam-393	700	11	∧	∧	PROPN
ejpam-393	700	12	i<3	i<3	NOUN
ejpam-393	700	13	pui	pui	PROPN
ejpam-393	700	14	(	(	PUNCT
ejpam-393	700	15	x	x	X
ejpam-393	700	16	i	i	PROPN
ejpam-393	700	17	)	)	PUNCT
ejpam-393	700	18	.	.	PUNCT
ejpam-393	701	1	then	then	ADV
ejpam-393	701	2	there	there	PRON
ejpam-393	701	3	exists	exist	VERB
ejpam-393	701	4	an	an	DET
ejpam-393	701	5	l	l	NOUN
ejpam-393	701	6	-	-	NOUN
ejpam-393	701	7	structure	structure	NOUN
ejpam-393	701	8	m	m	NOUN
ejpam-393	701	9	with	with	ADP
ejpam-393	701	10	the	the	DET
ejpam-393	701	11	following	follow	VERB
ejpam-393	701	12	properties	property	NOUN
ejpam-393	701	13	:	:	PUNCT
ejpam-393	701	14	(	(	PUNCT
ejpam-393	701	15	1	1	X
ejpam-393	701	16	)	)	PUNCT
ejpam-393	702	1	m	m	VERB
ejpam-393	702	2	has	have	VERB
ejpam-393	702	3	quantifier	quantifi	ADJ
ejpam-393	702	4	elimination	elimination	NOUN
ejpam-393	702	5	,	,	PUNCT
ejpam-393	702	6	i.e.	i.e.	X
ejpam-393	702	7	every	every	DET
ejpam-393	702	8	l	l	NOUN
ejpam-393	702	9	-	-	NOUN
ejpam-393	702	10	formula	formula	NOUN
ejpam-393	702	11	is	be	AUX
ejpam-393	702	12	equivalent	equivalent	ADJ
ejpam-393	702	13	in	in	ADP
ejpam-393	702	14	m	m	PROPN
ejpam-393	702	15	to	to	ADP
ejpam-393	702	16	a	a	DET
ejpam-393	702	17	boolean	boolean	ADJ
ejpam-393	702	18	combination	combination	NOUN
ejpam-393	702	19	of	of	ADP
ejpam-393	702	20	atomic	atomic	ADJ
ejpam-393	702	21	formulas	formula	NOUN
ejpam-393	702	22	.	.	PUNCT
ejpam-393	703	1	(	(	PUNCT
ejpam-393	703	2	2	2	X
ejpam-393	703	3	)	)	PUNCT
ejpam-393	703	4	the	the	DET
ejpam-393	703	5	sets	set	NOUN
ejpam-393	703	6	pm	pm	VERB
ejpam-393	703	7	i	i	PRON
ejpam-393	703	8	for	for	ADP
ejpam-393	703	9	i	i	PRON
ejpam-393	703	10	<	<	X
ejpam-393	703	11	3	3	NUM
ejpam-393	703	12	partition	partition	NOUN
ejpam-393	703	13	m	m	NOUN
ejpam-393	703	14	,	,	PUNCT
ejpam-393	703	15	(	(	PUNCT
ejpam-393	703	16	3	3	X
ejpam-393	703	17	)	)	PUNCT
ejpam-393	703	18	m	m	VERB
ejpam-393	703	19	|=	|=	VERB
ejpam-393	703	20	∀x0	∀x0	ADV
ejpam-393	703	21	x1	x1	PROPN
ejpam-393	703	22	x2(r(x0	x2(r(x0	X
ejpam-393	703	23	,	,	PUNCT
ejpam-393	703	24	x1	x1	PROPN
ejpam-393	703	25	x2)−→	x2)−→	PROPN
ejpam-393	703	26	∨	∨	NUM
ejpam-393	703	27	u∈s3	u∈s3	PROPN
ejpam-393	703	28	χu	χu	PROPN
ejpam-393	703	29	)	)	PUNCT
ejpam-393	703	30	,	,	PUNCT
ejpam-393	703	31	for	for	ADP
ejpam-393	703	32	all	all	DET
ejpam-393	703	33	r	r	NOUN
ejpam-393	703	34	∈	∈	PROPN
ejpam-393	703	35	l	l	NOUN
ejpam-393	703	36	,	,	PUNCT
ejpam-393	703	37	(	(	PUNCT
ejpam-393	703	38	4	4	X
ejpam-393	703	39	)	)	PUNCT
ejpam-393	703	40	m	m	NOUN
ejpam-393	703	41	|=	|=	NOUN
ejpam-393	703	42	∃x0	∃x0	PROPN
ejpam-393	703	43	x1	x1	PROPN
ejpam-393	703	44	x2(χu	x2(χu	PROPN
ejpam-393	703	45	∧	∧	PROPN
ejpam-393	703	46	r(x0	r(x0	NOUN
ejpam-393	703	47	,	,	PUNCT
ejpam-393	703	48	x1	x1	PROPN
ejpam-393	703	49	,	,	PUNCT
ejpam-393	703	50	x2	x2	ADJ
ejpam-393	703	51	)	)	PUNCT
ejpam-393	703	52	∧	∧	PROPN
ejpam-393	703	53	¬s(x0	¬s(x0	PROPN
ejpam-393	703	54	,	,	PUNCT
ejpam-393	703	55	x1	x1	PROPN
ejpam-393	703	56	,	,	PUNCT
ejpam-393	703	57	x2	x2	PROPN
ejpam-393	703	58	)	)	PUNCT
ejpam-393	703	59	)	)	PUNCT
ejpam-393	703	60	for	for	ADP
ejpam-393	703	61	all	all	DET
ejpam-393	703	62	distinct	distinct	ADJ
ejpam-393	703	63	ternary	ternary	ADJ
ejpam-393	703	64	r	r	NOUN
ejpam-393	703	65	,	,	PUNCT
ejpam-393	703	66	s	s	NOUN
ejpam-393	703	67	∈	∈	PROPN
ejpam-393	703	68	l	l	NOUN
ejpam-393	703	69	,	,	PUNCT
ejpam-393	703	70	and	and	CCONJ
ejpam-393	703	71	u	u	PROPN
ejpam-393	703	72	∈	∈	PROPN
ejpam-393	703	73	s3	s3	PROPN
ejpam-393	703	74	,	,	PUNCT
ejpam-393	703	75	(	(	PUNCT
ejpam-393	703	76	5	5	NUM
ejpam-393	703	77	)	)	PUNCT
ejpam-393	703	78	for	for	ADP
ejpam-393	703	79	u	u	PROPN
ejpam-393	703	80	∈	∈	PROPN
ejpam-393	703	81	s3	s3	PROPN
ejpam-393	703	82	,	,	PUNCT
ejpam-393	703	83	i	i	PRON
ejpam-393	703	84	<	<	X
ejpam-393	703	85	3	3	NUM
ejpam-393	703	86	,	,	PUNCT
ejpam-393	703	87	m	m	VERB
ejpam-393	703	88	|=	|=	VERB
ejpam-393	703	89	∀x0	∀x0	ADV
ejpam-393	703	90	x1	x1	PROPN
ejpam-393	703	91	x2(∃x	x2(∃x	PROPN
ejpam-393	703	92	iχu←→	iχu←→	ADJ
ejpam-393	703	93	∨	∨	NUM
ejpam-393	703	94	v∈33,v≡iu	v∈33,v≡iu	PROPN
ejpam-393	703	95	χv	χv	NOUN
ejpam-393	703	96	)	)	PUNCT
ejpam-393	703	97	,	,	PUNCT
ejpam-393	703	98	(	(	PUNCT
ejpam-393	703	99	6	6	NUM
ejpam-393	703	100	)	)	PUNCT
ejpam-393	703	101	for	for	ADP
ejpam-393	703	102	u	u	PROPN
ejpam-393	703	103	∈	∈	PROPN
ejpam-393	703	104	s3	s3	PROPN
ejpam-393	703	105	and	and	CCONJ
ejpam-393	703	106	any	any	DET
ejpam-393	703	107	l	l	NOUN
ejpam-393	703	108	-	-	NOUN
ejpam-393	703	109	formula	formula	NOUN
ejpam-393	703	110	φ(x0	φ(x0	NOUN
ejpam-393	703	111	,	,	PUNCT
ejpam-393	703	112	x1	x1	PROPN
ejpam-393	703	113	,	,	PUNCT
ejpam-393	703	114	x2	x2	PROPN
ejpam-393	703	115	)	)	PUNCT
ejpam-393	703	116	,	,	PUNCT
ejpam-393	703	117	if	if	SCONJ
ejpam-393	703	118	m	m	NOUN
ejpam-393	703	119	|=	|=	PUNCT
ejpam-393	703	120	∃x0	∃x0	PROPN
ejpam-393	703	121	x1	x1	PROPN
ejpam-393	703	122	x2(χu	x2(χu	PROPN
ejpam-393	703	123	∧φ	∧φ	PROPN
ejpam-393	703	124	)	)	PUNCT
ejpam-393	703	125	then	then	ADV
ejpam-393	703	126	m	m	VERB
ejpam-393	703	127	|=	|=	VERB
ejpam-393	703	128	∀x0	∀x0	ADV
ejpam-393	703	129	x1	x1	PROPN
ejpam-393	703	130	x2(∃x	x2(∃x	PROPN
ejpam-393	703	131	iχu←→∃x	iχu←→∃x	ADJ
ejpam-393	703	132	i(χu	i(χu	NOUN
ejpam-393	703	133	∧φ	∧φ	NOUN
ejpam-393	703	134	)	)	PUNCT
ejpam-393	703	135	)	)	PUNCT
ejpam-393	703	136	for	for	ADP
ejpam-393	703	137	all	all	PRON
ejpam-393	703	138	i	i	PRON
ejpam-393	703	139	<	<	X
ejpam-393	703	140	3	3	X
ejpam-393	703	141	.	.	PUNCT
ejpam-393	704	1	t.	t.	PROPN
ejpam-393	704	2	ahmed	ahmed	PROPN
ejpam-393	704	3	/	/	SYM
ejpam-393	704	4	eur	eur	PROPN
ejpam-393	704	5	.	.	PUNCT
ejpam-393	705	1	j.	j.	PROPN
ejpam-393	705	2	pure	pure	PROPN
ejpam-393	705	3	appl	appl	PROPN
ejpam-393	705	4	.	.	PROPN
ejpam-393	705	5	math	math	PROPN
ejpam-393	705	6	,	,	PUNCT
ejpam-393	705	7	3	3	NUM
ejpam-393	705	8	(	(	PUNCT
ejpam-393	705	9	2010	2010	NUM
ejpam-393	705	10	)	)	PUNCT
ejpam-393	705	11	,	,	PUNCT
ejpam-393	705	12	853	853	NUM
ejpam-393	705	13	-	-	SYM
ejpam-393	705	14	880	880	NUM
ejpam-393	705	15	870	870	NUM
ejpam-393	705	16	proof	proof	NOUN
ejpam-393	705	17	.	.	PUNCT
ejpam-393	706	1	throughout	throughout	ADP
ejpam-393	706	2	the	the	DET
ejpam-393	706	3	proof	proof	NOUN
ejpam-393	706	4	,	,	PUNCT
ejpam-393	706	5	we	we	PRON
ejpam-393	706	6	use	use	VERB
ejpam-393	706	7	the	the	DET
ejpam-393	706	8	notation	notation	NOUN
ejpam-393	706	9	x̄	x̄	NOUN
ejpam-393	706	10	,	,	PUNCT
ejpam-393	706	11	ā	ā	PROPN
ejpam-393	706	12	for	for	ADP
ejpam-393	706	13	finite	finite	ADJ
ejpam-393	706	14	sequences	sequence	NOUN
ejpam-393	706	15	,	,	PUNCT
ejpam-393	706	16	or	or	CCONJ
ejpam-393	706	17	tuples	tuple	VERB
ejpam-393	706	18	〈	〈	PROPN
ejpam-393	706	19	x0	x0	PROPN
ejpam-393	706	20	,	,	PUNCT
ejpam-393	706	21	·	·	PUNCT
ejpam-393	706	22	·	·	PUNCT
ejpam-393	706	23	·	·	PUNCT
ejpam-393	706	24	xm−1	xm−1	PROPN
ejpam-393	706	25	〉	〉	PROPN
ejpam-393	706	26	,	,	PUNCT
ejpam-393	706	27	〈	〈	NOUN
ejpam-393	706	28	a0	a0	NOUN
ejpam-393	706	29	,	,	PUNCT
ejpam-393	706	30	·	·	PUNCT
ejpam-393	706	31	·	·	PUNCT
ejpam-393	706	32	·	·	PUNCT
ejpam-393	706	33	am−1	am−1	NOUN
ejpam-393	706	34	〉	〉	NOUN
ejpam-393	706	35	.	.	PUNCT
ejpam-393	706	36	given	give	VERB
ejpam-393	706	37	a	a	DET
ejpam-393	706	38	structure	structure	NOUN
ejpam-393	706	39	m	m	NOUN
ejpam-393	706	40	and	and	CCONJ
ejpam-393	706	41	a	a	DET
ejpam-393	706	42	tuple	tuple	NOUN
ejpam-393	706	43	ā	ā	NOUN
ejpam-393	706	44	,	,	PUNCT
ejpam-393	706	45	we	we	PRON
ejpam-393	706	46	often	often	ADV
ejpam-393	706	47	write	write	VERB
ejpam-393	706	48	,	,	PUNCT
ejpam-393	706	49	with	with	ADP
ejpam-393	706	50	a	a	DET
ejpam-393	706	51	slight	slight	ADJ
ejpam-393	706	52	abuse	abuse	NOUN
ejpam-393	706	53	of	of	ADP
ejpam-393	706	54	notation	notation	NOUN
ejpam-393	706	55	,	,	PUNCT
ejpam-393	706	56	ā	ā	NOUN
ejpam-393	706	57	∈	∈	PROPN
ejpam-393	706	58	m	m	VERB
ejpam-393	706	59	instead	instead	ADV
ejpam-393	706	60	of	of	ADP
ejpam-393	706	61	ā	ā	PROPN
ejpam-393	706	62	∈	∈	PROPN
ejpam-393	706	63	mm	mm	INTJ
ejpam-393	706	64	,	,	PUNCT
ejpam-393	706	65	where	where	SCONJ
ejpam-393	706	66	m	m	NOUN
ejpam-393	706	67	is	be	AUX
ejpam-393	706	68	the	the	DET
ejpam-393	706	69	arity	arity	NOUN
ejpam-393	706	70	of	of	ADP
ejpam-393	706	71	the	the	DET
ejpam-393	706	72	tuple	tuple	NOUN
ejpam-393	706	73	ā.	ā.	PUNCT
ejpam-393	706	74	the	the	DET
ejpam-393	706	75	arity	arity	NOUN
ejpam-393	706	76	of	of	ADP
ejpam-393	706	77	tuples	tuple	NOUN
ejpam-393	706	78	will	will	AUX
ejpam-393	706	79	be	be	AUX
ejpam-393	706	80	clear	clear	ADJ
ejpam-393	706	81	from	from	ADP
ejpam-393	706	82	context	context	NOUN
ejpam-393	706	83	.	.	PUNCT
ejpam-393	707	1	let	let	VERB
ejpam-393	707	2	l	l	NOUN
ejpam-393	707	3	be	be	AUX
ejpam-393	707	4	the	the	DET
ejpam-393	707	5	relational	relational	ADJ
ejpam-393	707	6	signature	signature	NOUN
ejpam-393	707	7	containing	contain	VERB
ejpam-393	707	8	unary	unary	ADJ
ejpam-393	707	9	relation	relation	NOUN
ejpam-393	707	10	symbols	symbol	NOUN
ejpam-393	707	11	p0	p0	NOUN
ejpam-393	707	12	,	,	PUNCT
ejpam-393	707	13	.	.	PUNCT
ejpam-393	707	14	.	.	PUNCT
ejpam-393	708	1	.	.	PUNCT
ejpam-393	709	1	,	,	PUNCT
ejpam-393	709	2	p3	p3	PROPN
ejpam-393	709	3	and	and	CCONJ
ejpam-393	709	4	a	a	DET
ejpam-393	709	5	4	4	NUM
ejpam-393	709	6	-	-	PUNCT
ejpam-393	709	7	ary	ary	NOUN
ejpam-393	709	8	relation	relation	NOUN
ejpam-393	709	9	symbol	symbol	NOUN
ejpam-393	709	10	x	x	INTJ
ejpam-393	709	11	.	.	PUNCT
ejpam-393	710	1	let	let	VERB
ejpam-393	710	2	k	k	X
ejpam-393	710	3	be	be	AUX
ejpam-393	710	4	the	the	DET
ejpam-393	710	5	class	class	NOUN
ejpam-393	710	6	of	of	ADP
ejpam-393	710	7	all	all	DET
ejpam-393	710	8	finite	finite	ADJ
ejpam-393	710	9	l	l	PROPN
ejpam-393	710	10	-structures	-structures	PROPN
ejpam-393	710	11	d	d	ADP
ejpam-393	710	12	satsfying	satsfye	VERB
ejpam-393	710	13	the	the	DET
ejpam-393	710	14	pi	pi	NOUN
ejpam-393	710	15	’s	’s	PART
ejpam-393	710	16	are	be	AUX
ejpam-393	710	17	disjoint	disjoint	ADJ
ejpam-393	710	18	:	:	PUNCT
ejpam-393	710	19	∀x	∀x	X
ejpam-393	710	20	∨	∨	NUM
ejpam-393	710	21	i	i	PRON
ejpam-393	710	22	<	<	X
ejpam-393	710	23	j<4	j<4	PROPN
ejpam-393	711	1	(	(	PUNCT
ejpam-393	711	2	pi(x)∧	pi(x)∧	VERB
ejpam-393	711	3	∧	∧	PROPN
ejpam-393	711	4	j	j	PROPN
ejpam-393	711	5	6	6	NUM
ejpam-393	711	6	=	=	NOUN
ejpam-393	711	7	i	i	PRON
ejpam-393	711	8	¬pj(x	¬pj(x	ADJ
ejpam-393	711	9	)	)	PUNCT
ejpam-393	711	10	)	)	PUNCT
ejpam-393	711	11	.	.	PUNCT
ejpam-393	712	1	(	(	PUNCT
ejpam-393	712	2	6	6	X
ejpam-393	712	3	)	)	PUNCT
ejpam-393	712	4	∀x0	∀x0	NOUN
ejpam-393	712	5	·	·	PUNCT
ejpam-393	712	6	·	·	PUNCT
ejpam-393	712	7	·	·	PUNCT
ejpam-393	713	1	x3(x	x3(x	PUNCT
ejpam-393	713	2	(	(	PUNCT
ejpam-393	713	3	x0	x0	PROPN
ejpam-393	713	4	,	,	PUNCT
ejpam-393	713	5	·	·	PUNCT
ejpam-393	713	6	·	·	PUNCT
ejpam-393	713	7	·	·	PUNCT
ejpam-393	713	8	,	,	PUNCT
ejpam-393	713	9	x3)−→	x3)−→	PROPN
ejpam-393	714	1	p3(x3)∧	p3(x3)∧	PROPN
ejpam-393	714	2	∨	∨	PROPN
ejpam-393	714	3	u∈s3	u∈s3	PROPN
ejpam-393	714	4	χu	χu	PROPN
ejpam-393	714	5	)	)	PUNCT
ejpam-393	714	6	.	.	PUNCT
ejpam-393	715	1	(	(	PUNCT
ejpam-393	715	2	7	7	X
ejpam-393	715	3	)	)	PUNCT
ejpam-393	715	4	then	then	ADV
ejpam-393	715	5	k	k	PROPN
ejpam-393	715	6	contains	contain	VERB
ejpam-393	715	7	countably	countably	ADV
ejpam-393	715	8	many	many	ADJ
ejpam-393	715	9	isomorphism	isomorphism	NOUN
ejpam-393	715	10	types	type	NOUN
ejpam-393	715	11	,	,	PUNCT
ejpam-393	715	12	because	because	SCONJ
ejpam-393	715	13	for	for	ADP
ejpam-393	715	14	each	each	DET
ejpam-393	715	15	n	n	ADV
ejpam-393	715	16	∈ω	∈ω	NOUN
ejpam-393	715	17	,	,	PUNCT
ejpam-393	715	18	there	there	PRON
ejpam-393	715	19	are	be	VERB
ejpam-393	715	20	countably	countably	ADV
ejpam-393	715	21	many	many	ADJ
ejpam-393	715	22	isomorphism	isomorphism	NOUN
ejpam-393	715	23	types	type	NOUN
ejpam-393	715	24	of	of	ADP
ejpam-393	715	25	finite	finite	ADJ
ejpam-393	715	26	l	l	PROPN
ejpam-393	715	27	structures	structure	NOUN
ejpam-393	715	28	(	(	PUNCT
ejpam-393	715	29	satifying	satifye	VERB
ejpam-393	715	30	(	(	PUNCT
ejpam-393	715	31	6	6	NUM
ejpam-393	715	32	)	)	PUNCT
ejpam-393	715	33	and	and	CCONJ
ejpam-393	715	34	(	(	PUNCT
ejpam-393	715	35	7	7	NUM
ejpam-393	715	36	)	)	PUNCT
ejpam-393	715	37	)	)	PUNCT
ejpam-393	716	1	having	have	VERB
ejpam-393	716	2	cardinality	cardinality	NOUN
ejpam-393	716	3	≤	≤	NUM
ejpam-393	716	4	n.	n.	NOUN
ejpam-393	716	5	also	also	ADV
ejpam-393	716	6	it	it	PRON
ejpam-393	716	7	is	be	AUX
ejpam-393	716	8	easy	easy	ADJ
ejpam-393	716	9	to	to	PART
ejpam-393	716	10	check	check	VERB
ejpam-393	716	11	that	that	SCONJ
ejpam-393	716	12	k	k	PROPN
ejpam-393	716	13	is	be	AUX
ejpam-393	716	14	closed	close	VERB
ejpam-393	716	15	under	under	ADP
ejpam-393	716	16	substructures	substructure	NOUN
ejpam-393	716	17	and	and	CCONJ
ejpam-393	716	18	that	that	SCONJ
ejpam-393	716	19	k	k	PROPN
ejpam-393	716	20	has	have	VERB
ejpam-393	716	21	the	the	DET
ejpam-393	716	22	ap	ap	PROPN
ejpam-393	716	23	.	.	PROPN
ejpam-393	717	1	from	from	ADP
ejpam-393	717	2	the	the	DET
ejpam-393	717	3	latter	latter	ADJ
ejpam-393	717	4	it	it	PRON
ejpam-393	717	5	follows	follow	VERB
ejpam-393	717	6	that	that	SCONJ
ejpam-393	717	7	it	it	PRON
ejpam-393	717	8	has	have	VERB
ejpam-393	717	9	the	the	DET
ejpam-393	717	10	j	j	PROPN
ejpam-393	717	11	ep	ep	PROPN
ejpam-393	717	12	,	,	PUNCT
ejpam-393	717	13	since	since	SCONJ
ejpam-393	717	14	k	k	PROPN
ejpam-393	717	15	contains	contain	VERB
ejpam-393	717	16	the	the	DET
ejpam-393	717	17	one	one	NUM
ejpam-393	717	18	element	element	NOUN
ejpam-393	717	19	structure	structure	NOUN
ejpam-393	717	20	that	that	PRON
ejpam-393	717	21	is	be	AUX
ejpam-393	717	22	embeddable	embeddable	ADJ
ejpam-393	717	23	in	in	ADP
ejpam-393	717	24	any	any	DET
ejpam-393	717	25	structure	structure	NOUN
ejpam-393	717	26	in	in	ADP
ejpam-393	717	27	k.	k.	PROPN
ejpam-393	717	28	∗	∗	PROPN
ejpam-393	717	29	then	then	ADV
ejpam-393	717	30	there	there	PRON
ejpam-393	717	31	is	be	VERB
ejpam-393	717	32	a	a	DET
ejpam-393	717	33	countably	countably	ADV
ejpam-393	717	34	infinite	infinite	ADJ
ejpam-393	717	35	homogeneous	homogeneous	ADJ
ejpam-393	717	36	l	l	NOUN
ejpam-393	717	37	structure	structure	NOUN
ejpam-393	717	38	n	n	CCONJ
ejpam-393	717	39	with	with	ADP
ejpam-393	717	40	age	age	NOUN
ejpam-393	717	41	k.	k.	PROPN
ejpam-393	717	42	n	n	PROPN
ejpam-393	717	43	has	have	VERB
ejpam-393	717	44	quantifier	quantifi	ADJ
ejpam-393	717	45	elimination	elimination	NOUN
ejpam-393	717	46	,	,	PUNCT
ejpam-393	717	47	and	and	CCONJ
ejpam-393	717	48	obviously	obviously	ADV
ejpam-393	717	49	,	,	PUNCT
ejpam-393	717	50	so	so	ADV
ejpam-393	717	51	does	do	AUX
ejpam-393	717	52	any	any	DET
ejpam-393	717	53	elementary	elementary	ADJ
ejpam-393	717	54	extension	extension	NOUN
ejpam-393	717	55	of	of	ADP
ejpam-393	717	56	n.	n.	PROPN
ejpam-393	717	57	k	k	PROPN
ejpam-393	717	58	contains	contain	VERB
ejpam-393	717	59	structures	structure	NOUN
ejpam-393	717	60	with	with	ADP
ejpam-393	717	61	arbitrarily	arbitrarily	ADV
ejpam-393	717	62	large	large	ADJ
ejpam-393	717	63	p3	p3	NOUN
ejpam-393	717	64	-	-	PUNCT
ejpam-393	717	65	part	part	NOUN
ejpam-393	717	66	,	,	PUNCT
ejpam-393	717	67	so	so	CCONJ
ejpam-393	717	68	pn	pn	PROPN
ejpam-393	717	69	3	3	NUM
ejpam-393	717	70	is	be	AUX
ejpam-393	717	71	infinite	infinite	ADJ
ejpam-393	717	72	.	.	PUNCT
ejpam-393	718	1	let	let	VERB
ejpam-393	718	2	n∗	n∗	PROPN
ejpam-393	718	3	be	be	AUX
ejpam-393	718	4	an	an	DET
ejpam-393	718	5	elementary	elementary	ADJ
ejpam-393	718	6	extension	extension	NOUN
ejpam-393	718	7	of	of	ADP
ejpam-393	718	8	n	n	PRON
ejpam-393	718	9	such	such	ADJ
ejpam-393	718	10	that	that	SCONJ
ejpam-393	718	11	|pn	|pn	X
ejpam-393	718	12	∗	∗	NOUN
ejpam-393	718	13	3	3	NUM
ejpam-393	719	1	|	|	NOUN
ejpam-393	719	2	=	=	PUNCT
ejpam-393	719	3	|l|	|l|	NOUN
ejpam-393	719	4	,	,	PUNCT
ejpam-393	719	5	and	and	CCONJ
ejpam-393	719	6	fix	fix	VERB
ejpam-393	719	7	a	a	DET
ejpam-393	719	8	bijection	bijection	NOUN
ejpam-393	719	9	∗	∗	NOUN
ejpam-393	719	10	from	from	ADP
ejpam-393	719	11	the	the	DET
ejpam-393	719	12	set	set	NOUN
ejpam-393	719	13	of	of	ADP
ejpam-393	719	14	ternary	ternary	ADJ
ejpam-393	719	15	relation	relation	NOUN
ejpam-393	719	16	symbols	symbol	NOUN
ejpam-393	719	17	of	of	ADP
ejpam-393	719	18	l	l	NOUN
ejpam-393	719	19	to	to	ADP
ejpam-393	719	20	pn	pn	PROPN
ejpam-393	719	21	∗	∗	PROPN
ejpam-393	719	22	3	3	NUM
ejpam-393	719	23	.	.	PUNCT
ejpam-393	720	1	define	define	VERB
ejpam-393	720	2	an	an	DET
ejpam-393	720	3	l	l	NOUN
ejpam-393	720	4	-	-	NOUN
ejpam-393	720	5	structure	structure	NOUN
ejpam-393	720	6	m	m	NOUN
ejpam-393	720	7	with	with	ADP
ejpam-393	720	8	domain	domain	NOUN
ejpam-393	720	9	pn	pn	PROPN
ejpam-393	720	10	∗	∗	X
ejpam-393	720	11	0	0	PUNCT
ejpam-393	720	12	∪	∪	ADP
ejpam-393	720	13	pn	pn	PROPN
ejpam-393	720	14	∗	∗	NOUN
ejpam-393	720	15	1	1	NUM
ejpam-393	720	16	∪	∪	ADP
ejpam-393	720	17	pn	pn	PROPN
ejpam-393	720	18	∗	∗	X
ejpam-393	720	19	2	2	NUM
ejpam-393	720	20	,	,	PUNCT
ejpam-393	720	21	by	by	ADP
ejpam-393	720	22	:	:	PUNCT
ejpam-393	720	23	pm	pm	NOUN
ejpam-393	721	1	i	i	PRON
ejpam-393	721	2	=	=	PUNCT
ejpam-393	722	1	pn	pn	PROPN
ejpam-393	722	2	∗	∗	NOUN
ejpam-393	722	3	i	i	PRON
ejpam-393	722	4	for	for	ADP
ejpam-393	722	5	i	i	PRON
ejpam-393	722	6	<	<	X
ejpam-393	722	7	3	3	NUM
ejpam-393	722	8	and	and	CCONJ
ejpam-393	722	9	for	for	ADP
ejpam-393	722	10	ternary	ternary	ADJ
ejpam-393	722	11	r	r	NOUN
ejpam-393	722	12	∈	∈	PROPN
ejpam-393	722	13	l	l	NOUN
ejpam-393	722	14	,	,	PUNCT
ejpam-393	722	15	m	m	VERB
ejpam-393	722	16	|=	|=	PUNCT
ejpam-393	722	17	r(a0	r(a0	NOUN
ejpam-393	722	18	,	,	PUNCT
ejpam-393	722	19	a1	a1	NOUN
ejpam-393	722	20	,	,	PUNCT
ejpam-393	722	21	a2	a2	PROPN
ejpam-393	722	22	)	)	PUNCT
ejpam-393	722	23	iff	iff	PROPN
ejpam-393	722	24	n∗	n∗	PROPN
ejpam-393	722	25	|=	|=	PUNCT
ejpam-393	722	26	x	x	X
ejpam-393	722	27	(	(	PUNCT
ejpam-393	722	28	a0	a0	NOUN
ejpam-393	722	29	,	,	PUNCT
ejpam-393	722	30	a1	a1	NOUN
ejpam-393	722	31	,	,	PUNCT
ejpam-393	722	32	a2,r∗	a2,r∗	PROPN
ejpam-393	722	33	)	)	PUNCT
ejpam-393	722	34	.	.	PUNCT
ejpam-393	723	1	if	if	SCONJ
ejpam-393	723	2	φ	φ	PROPN
ejpam-393	723	3	(	(	PUNCT
ejpam-393	723	4	x̄	x̄	PROPN
ejpam-393	723	5	)	)	PUNCT
ejpam-393	723	6	is	be	AUX
ejpam-393	723	7	any	any	DET
ejpam-393	723	8	l	l	NOUN
ejpam-393	723	9	-	-	NOUN
ejpam-393	723	10	formula	formula	NOUN
ejpam-393	723	11	,	,	PUNCT
ejpam-393	723	12	let	let	VERB
ejpam-393	723	13	φ∗	φ∗	NOUN
ejpam-393	723	14	(	(	PUNCT
ejpam-393	723	15	x̄	x̄	NOUN
ejpam-393	723	16	,	,	PUNCT
ejpam-393	723	17	r̄	r̄	NOUN
ejpam-393	723	18	)	)	PUNCT
ejpam-393	723	19	be	be	VERB
ejpam-393	723	20	the	the	DET
ejpam-393	723	21	l	l	NOUN
ejpam-393	723	22	-formula	-formula	NOUN
ejpam-393	723	23	with	with	ADP
ejpam-393	723	24	parameters	parameter	NOUN
ejpam-393	723	25	r̄	r̄	NOUN
ejpam-393	723	26	from	from	ADP
ejpam-393	723	27	n	n	DET
ejpam-393	723	28	∗	∗	NOUN
ejpam-393	723	29	obtained	obtain	VERB
ejpam-393	723	30	from	from	ADP
ejpam-393	723	31	φ	φ	NUM
ejpam-393	723	32	by	by	ADP
ejpam-393	723	33	replacing	replace	VERB
ejpam-393	723	34	each	each	DET
ejpam-393	723	35	atomic	atomic	ADJ
ejpam-393	723	36	subformula	subformula	NOUN
ejpam-393	723	37	r(x	r(x	PROPN
ejpam-393	723	38	,	,	PUNCT
ejpam-393	723	39	y	y	PROPN
ejpam-393	723	40	,	,	PUNCT
ejpam-393	723	41	z	z	NOUN
ejpam-393	723	42	)	)	PUNCT
ejpam-393	723	43	by	by	ADP
ejpam-393	723	44	x	x	X
ejpam-393	723	45	(	(	PUNCT
ejpam-393	723	46	x	x	INTJ
ejpam-393	723	47	,	,	PUNCT
ejpam-393	723	48	y	y	PROPN
ejpam-393	723	49	,	,	PUNCT
ejpam-393	723	50	z	z	PROPN
ejpam-393	723	51	,	,	PUNCT
ejpam-393	723	52	r∗	r∗	PROPN
ejpam-393	723	53	)	)	PUNCT
ejpam-393	723	54	and	and	CCONJ
ejpam-393	723	55	relativizing	relativize	VERB
ejpam-393	723	56	quantifiers	quantifier	NOUN
ejpam-393	723	57	to	to	ADP
ejpam-393	723	58	¬p3	¬p3	PROPN
ejpam-393	723	59	,	,	PUNCT
ejpam-393	723	60	that	that	PRON
ejpam-393	723	61	is	be	AUX
ejpam-393	723	62	replacing	replace	VERB
ejpam-393	723	63	(	(	PUNCT
ejpam-393	723	64	∃x)φ(x	∃x)φ(x	NOUN
ejpam-393	723	65	)	)	PUNCT
ejpam-393	723	66	and	and	CCONJ
ejpam-393	723	67	(	(	PUNCT
ejpam-393	723	68	∀x)φ(x	∀x)φ(x	NOUN
ejpam-393	723	69	)	)	PUNCT
ejpam-393	723	70	by	by	ADP
ejpam-393	723	71	(	(	PUNCT
ejpam-393	723	72	∃x)(¬p3(x	∃x)(¬p3(x	PROPN
ejpam-393	723	73	)	)	PUNCT
ejpam-393	723	74	→	→	SYM
ejpam-393	723	75	φ(x	φ(x	NOUN
ejpam-393	723	76	)	)	PUNCT
ejpam-393	723	77	)	)	PUNCT
ejpam-393	723	78	and	and	CCONJ
ejpam-393	723	79	(	(	PUNCT
ejpam-393	723	80	∀x)(¬p3(x	∀x)(¬p3(x	PROPN
ejpam-393	723	81	)	)	PUNCT
ejpam-393	723	82	→	→	SYM
ejpam-393	723	83	φ(x	φ(x	NOUN
ejpam-393	723	84	)	)	PUNCT
ejpam-393	723	85	)	)	PUNCT
ejpam-393	723	86	,	,	PUNCT
ejpam-393	723	87	respectively	respectively	ADV
ejpam-393	723	88	.	.	PUNCT
ejpam-393	724	1	a	a	DET
ejpam-393	724	2	straightforward	straightforward	ADJ
ejpam-393	724	3	induction	induction	NOUN
ejpam-393	724	4	on	on	ADP
ejpam-393	724	5	complexity	complexity	NOUN
ejpam-393	724	6	of	of	ADP
ejpam-393	724	7	formulas	formula	NOUN
ejpam-393	724	8	gives	give	VERB
ejpam-393	724	9	that	that	PRON
ejpam-393	724	10	for	for	ADP
ejpam-393	724	11	ā	ā	ADJ
ejpam-393	724	12	∈m	∈m	NOUN
ejpam-393	724	13	m	m	PRON
ejpam-393	724	14	|=	|=	NOUN
ejpam-393	724	15	φ(ā	φ(ā	NUM
ejpam-393	724	16	)	)	PUNCT
ejpam-393	724	17	iff	iff	PROPN
ejpam-393	724	18	n∗	n∗	PROPN
ejpam-393	724	19	|=	|=	PUNCT
ejpam-393	724	20	φ∗(ā	φ∗(ā	PROPN
ejpam-393	724	21	,	,	PUNCT
ejpam-393	724	22	r̄	r̄	NOUN
ejpam-393	724	23	)	)	PUNCT
ejpam-393	724	24	.	.	PUNCT
ejpam-393	725	1	we	we	PRON
ejpam-393	725	2	show	show	VERB
ejpam-393	725	3	that	that	SCONJ
ejpam-393	725	4	m	m	NOUN
ejpam-393	725	5	is	be	AUX
ejpam-393	725	6	as	as	SCONJ
ejpam-393	725	7	required	require	VERB
ejpam-393	725	8	.	.	PUNCT
ejpam-393	726	1	for	for	ADP
ejpam-393	726	2	quantifier	quantifier	NOUN
ejpam-393	726	3	elimination	elimination	NOUN
ejpam-393	726	4	,	,	PUNCT
ejpam-393	726	5	if	if	SCONJ
ejpam-393	726	6	φ	φ	PROPN
ejpam-393	726	7	(	(	PUNCT
ejpam-393	726	8	x̄	x̄	PROPN
ejpam-393	726	9	)	)	PUNCT
ejpam-393	726	10	is	be	AUX
ejpam-393	726	11	an	an	DET
ejpam-393	726	12	l	l	NOUN
ejpam-393	726	13	-	-	NOUN
ejpam-393	726	14	formula	formula	NOUN
ejpam-393	726	15	,	,	PUNCT
ejpam-393	726	16	then	then	ADV
ejpam-393	726	17	φ∗	φ∗	PROPN
ejpam-393	726	18	(	(	PUNCT
ejpam-393	726	19	x̄	x̄	NOUN
ejpam-393	726	20	,	,	PUNCT
ejpam-393	726	21	r̄∗	r̄∗	NOUN
ejpam-393	726	22	)	)	PUNCT
ejpam-393	726	23	is	be	AUX
ejpam-393	726	24	equivalent	equivalent	ADJ
ejpam-393	726	25	in	in	ADP
ejpam-393	726	26	n	n	ADP
ejpam-393	726	27	∗	∗	NOUN
ejpam-393	726	28	to	to	ADP
ejpam-393	726	29	a	a	DET
ejpam-393	726	30	quantifier	quantifier	NOUN
ejpam-393	726	31	free	free	ADJ
ejpam-393	726	32	l	l	NOUN
ejpam-393	726	33	-formula	-formula	PROPN
ejpam-393	726	34	ψ	ψ	X
ejpam-393	726	35	(	(	PUNCT
ejpam-393	726	36	x̄	x̄	NOUN
ejpam-393	726	37	,	,	PUNCT
ejpam-393	726	38	r̄∗	r̄∗	PROPN
ejpam-393	726	39	)	)	PUNCT
ejpam-393	726	40	.	.	PUNCT
ejpam-393	727	1	then	then	ADV
ejpam-393	727	2	replacing	replace	VERB
ejpam-393	727	3	ψ	ψ	PART
ejpam-393	727	4	’s	’s	PART
ejpam-393	727	5	atomic	atomic	ADJ
ejpam-393	727	6	subformulas	subformula	NOUN
ejpam-393	727	7	x	x	SYM
ejpam-393	727	8	(	(	PUNCT
ejpam-393	727	9	x	x	X
ejpam-393	727	10	,	,	PUNCT
ejpam-393	727	11	y	y	PROPN
ejpam-393	727	12	,	,	PUNCT
ejpam-393	727	13	z	z	PROPN
ejpam-393	727	14	,	,	PUNCT
ejpam-393	727	15	r∗	r∗	PROPN
ejpam-393	727	16	)	)	PUNCT
ejpam-393	727	17	by	by	ADP
ejpam-393	727	18	r(x	r(x	PROPN
ejpam-393	727	19	,	,	PUNCT
ejpam-393	727	20	y	y	PROPN
ejpam-393	727	21	,	,	PUNCT
ejpam-393	727	22	z	z	NOUN
ejpam-393	727	23	)	)	PUNCT
ejpam-393	727	24	,	,	PUNCT
ejpam-393	727	25	replacing	replace	VERB
ejpam-393	727	26	all	all	DET
ejpam-393	727	27	x	x	PUNCT
ejpam-393	727	28	(	(	PUNCT
ejpam-393	727	29	t0	t0	NOUN
ejpam-393	727	30	,	,	PUNCT
ejpam-393	727	31	·	·	PUNCT
ejpam-393	727	32	·	·	PUNCT
ejpam-393	727	33	·	·	PUNCT
ejpam-393	727	34	t3	t3	NOUN
ejpam-393	727	35	)	)	PUNCT
ejpam-393	727	36	not	not	PART
ejpam-393	727	37	of	of	ADP
ejpam-393	727	38	this	this	DET
ejpam-393	727	39	form	form	NOUN
ejpam-393	727	40	by	by	ADP
ejpam-393	727	41	⊥	⊥	PROPN
ejpam-393	727	42	,	,	PUNCT
ejpam-393	727	43	replacing	replace	VERB
ejpam-393	727	44	subformulas	subformulas	ADP
ejpam-393	727	45	p3(x	p3(x	PROPN
ejpam-393	727	46	)	)	PUNCT
ejpam-393	727	47	by	by	ADP
ejpam-393	727	48	⊥	⊥	NOUN
ejpam-393	727	49	,	,	PUNCT
ejpam-393	727	50	and	and	CCONJ
ejpam-393	727	51	pi(r	pi(r	NOUN
ejpam-393	727	52	∗	∗	NOUN
ejpam-393	727	53	)	)	PUNCT
ejpam-393	727	54	by	by	ADP
ejpam-393	727	55	⊥	⊥	PROPN
ejpam-393	728	1	if	if	SCONJ
ejpam-393	728	2	i	i	PRON
ejpam-393	728	3	<	<	X
ejpam-393	728	4	3	3	NUM
ejpam-393	728	5	and	and	CCONJ
ejpam-393	728	6	⊤	⊤	NOUN
ejpam-393	728	7	if	if	SCONJ
ejpam-393	728	8	i	i	PRON
ejpam-393	728	9	=	=	NOUN
ejpam-393	728	10	3	3	NUM
ejpam-393	728	11	,	,	PUNCT
ejpam-393	728	12	gives	give	VERB
ejpam-393	728	13	a	a	DET
ejpam-393	728	14	quantifier	quantifier	NOUN
ejpam-393	728	15	free	free	ADJ
ejpam-393	728	16	l	l	NOUN
ejpam-393	728	17	-formula	-formula	PROPN
ejpam-393	728	18	ψ	ψ	X
ejpam-393	728	19	equivalent	equivalent	NOUN
ejpam-393	728	20	in	in	ADP
ejpam-393	728	21	m	m	PROPN
ejpam-393	728	22	to	to	ADP
ejpam-393	728	23	φ	φ	NUM
ejpam-393	728	24	.	.	PUNCT
ejpam-393	729	1	for	for	ADP
ejpam-393	729	2	(	(	PUNCT
ejpam-393	729	3	2	2	NUM
ejpam-393	729	4	)	)	PUNCT
ejpam-393	729	5	,	,	PUNCT
ejpam-393	729	6	let	let	VERB
ejpam-393	729	7	σ	σ	NOUN
ejpam-393	729	8	=	=	SYM
ejpam-393	729	9	∀x(¬p3(x)−→	∀x(¬p3(x)−→	PROPN
ejpam-393	729	10	∨	∨	NUM
ejpam-393	729	11	i<3	i<3	NOUN
ejpam-393	729	12	(	(	PUNCT
ejpam-393	729	13	pi(x)∧	pi(x)∧	VERB
ejpam-393	729	14	∧	∧	PROPN
ejpam-393	729	15	j	j	PROPN
ejpam-393	729	16	6	6	NUM
ejpam-393	729	17	=	=	NOUN
ejpam-393	729	18	i	i	PRON
ejpam-393	729	19	¬pj(x	¬pj(x	ADJ
ejpam-393	729	20	)	)	PUNCT
ejpam-393	729	21	)	)	PUNCT
ejpam-393	729	22	)	)	PUNCT
ejpam-393	729	23	.	.	PUNCT
ejpam-393	730	1	then	then	ADV
ejpam-393	730	2	k	k	X
ejpam-393	730	3	|=	|=	PROPN
ejpam-393	730	4	σ	σ	PROPN
ejpam-393	730	5	,	,	PUNCT
ejpam-393	730	6	so	so	CCONJ
ejpam-393	730	7	n	n	NUM
ejpam-393	730	8	|=	|=	X
ejpam-393	730	9	σ	σ	NOUN
ejpam-393	730	10	and	and	CCONJ
ejpam-393	730	11	n	n	NOUN
ejpam-393	730	12	∗	∗	NOUN
ejpam-393	730	13	|=	|=	X
ejpam-393	730	14	σ	σ	X
ejpam-393	730	15	.	.	PUNCT
ejpam-393	731	1	it	it	PRON
ejpam-393	731	2	follows	follow	VERB
ejpam-393	731	3	from	from	ADP
ejpam-393	731	4	the	the	DET
ejpam-393	731	5	definition	definition	NOUN
ejpam-393	731	6	that	that	PRON
ejpam-393	731	7	m	m	VERB
ejpam-393	731	8	satisfies	satisfie	NOUN
ejpam-393	731	9	(	(	PUNCT
ejpam-393	731	10	2	2	NUM
ejpam-393	731	11	)	)	PUNCT
ejpam-393	731	12	;	;	PUNCT
ejpam-393	731	13	(	(	PUNCT
ejpam-393	731	14	3	3	X
ejpam-393	731	15	)	)	PUNCT
ejpam-393	731	16	is	be	AUX
ejpam-393	731	17	similar	similar	ADJ
ejpam-393	731	18	.	.	PUNCT
ejpam-393	732	1	∗it	∗it	PUNCT
ejpam-393	732	2	is	be	AUX
ejpam-393	732	3	not	not	PART
ejpam-393	732	4	always	always	ADV
ejpam-393	732	5	true	true	ADJ
ejpam-393	732	6	that	that	SCONJ
ejpam-393	732	7	ap	ap	PROPN
ejpam-393	732	8	implies	imply	VERB
ejpam-393	732	9	j	j	PROPN
ejpam-393	732	10	ep	ep	PROPN
ejpam-393	732	11	;	;	PUNCT
ejpam-393	732	12	think	think	VERB
ejpam-393	732	13	of	of	ADP
ejpam-393	732	14	fields	field	NOUN
ejpam-393	732	15	.	.	PUNCT
ejpam-393	733	1	t.	t.	PROPN
ejpam-393	733	2	ahmed	ahmed	PROPN
ejpam-393	733	3	/	/	SYM
ejpam-393	733	4	eur	eur	PROPN
ejpam-393	733	5	.	.	PUNCT
ejpam-393	734	1	j.	j.	PROPN
ejpam-393	734	2	pure	pure	PROPN
ejpam-393	734	3	appl	appl	PROPN
ejpam-393	734	4	.	.	PROPN
ejpam-393	734	5	math	math	PROPN
ejpam-393	734	6	,	,	PUNCT
ejpam-393	734	7	3	3	NUM
ejpam-393	734	8	(	(	PUNCT
ejpam-393	734	9	2010	2010	NUM
ejpam-393	734	10	)	)	PUNCT
ejpam-393	734	11	,	,	PUNCT
ejpam-393	734	12	853	853	NUM
ejpam-393	734	13	-	-	SYM
ejpam-393	734	14	880	880	NUM
ejpam-393	734	15	871	871	NUM
ejpam-393	734	16	for	for	ADP
ejpam-393	734	17	(	(	PUNCT
ejpam-393	734	18	4	4	NUM
ejpam-393	734	19	)	)	PUNCT
ejpam-393	734	20	,	,	PUNCT
ejpam-393	734	21	let	let	VERB
ejpam-393	734	22	u	u	PRON
ejpam-393	734	23	∈	∈	PROPN
ejpam-393	734	24	s3	s3	PROPN
ejpam-393	734	25	and	and	CCONJ
ejpam-393	734	26	let	let	VERB
ejpam-393	734	27	r	r	NOUN
ejpam-393	734	28	,	,	PUNCT
ejpam-393	734	29	s	s	PART
ejpam-393	734	30	∈	∈	NOUN
ejpam-393	734	31	pm	pm	NOUN
ejpam-393	734	32	3	3	NUM
ejpam-393	734	33	be	be	AUX
ejpam-393	734	34	distinct	distinct	ADJ
ejpam-393	734	35	.	.	PUNCT
ejpam-393	735	1	take	take	VERB
ejpam-393	735	2	a	a	DET
ejpam-393	735	3	finite	finite	ADJ
ejpam-393	735	4	l	l	NOUN
ejpam-393	735	5	-structure	-structure	NOUN
ejpam-393	735	6	d	d	NOUN
ejpam-393	735	7	with	with	ADP
ejpam-393	735	8	points	point	NOUN
ejpam-393	735	9	ai	ai	VERB
ejpam-393	735	10	∈	∈	PROPN
ejpam-393	735	11	pd	pd	PROPN
ejpam-393	735	12	ui	ui	PROPN
ejpam-393	736	1	(	(	PUNCT
ejpam-393	736	2	i	i	PRON
ejpam-393	736	3	<	<	X
ejpam-393	736	4	3	3	NUM
ejpam-393	736	5	)	)	PUNCT
ejpam-393	736	6	and	and	CCONJ
ejpam-393	736	7	distinct	distinct	ADJ
ejpam-393	736	8	r	r	NOUN
ejpam-393	736	9	′	′	NOUN
ejpam-393	736	10	,	,	PUNCT
ejpam-393	736	11	s′	s′	PROPN
ejpam-393	736	12	∈	∈	PROPN
ejpam-393	736	13	pd	pd	NOUN
ejpam-393	736	14	3	3	NUM
ejpam-393	736	15	with	with	ADP
ejpam-393	736	16	d	d	PROPN
ejpam-393	736	17	|=	|=	PUNCT
ejpam-393	736	18	x	x	SYM
ejpam-393	736	19	(	(	PUNCT
ejpam-393	736	20	a0	a0	NOUN
ejpam-393	736	21	,	,	PUNCT
ejpam-393	736	22	a1	a1	PROPN
ejpam-393	736	23	,	,	PUNCT
ejpam-393	736	24	a2	a2	PROPN
ejpam-393	736	25	,	,	PUNCT
ejpam-393	736	26	r	r	NOUN
ejpam-393	736	27	′)∧¬x	′)∧¬x	NUM
ejpam-393	736	28	(	(	PUNCT
ejpam-393	736	29	a0	a0	NOUN
ejpam-393	736	30	,	,	PUNCT
ejpam-393	736	31	a1	a1	PROPN
ejpam-393	736	32	,	,	PUNCT
ejpam-393	736	33	a2	a2	PROPN
ejpam-393	736	34	,	,	PUNCT
ejpam-393	736	35	s′	s′	NOUN
ejpam-393	736	36	)	)	PUNCT
ejpam-393	736	37	.	.	PUNCT
ejpam-393	737	1	then	then	ADV
ejpam-393	737	2	d	d	PROPN
ejpam-393	737	3	∈	∈	PROPN
ejpam-393	737	4	k	k	NOUN
ejpam-393	737	5	,	,	PUNCT
ejpam-393	737	6	so	so	ADV
ejpam-393	737	7	d	d	X
ejpam-393	737	8	embeds	embed	VERB
ejpam-393	737	9	into	into	ADP
ejpam-393	737	10	n.	n.	NOUN
ejpam-393	737	11	by	by	ADP
ejpam-393	737	12	homogeneity	homogeneity	NOUN
ejpam-393	737	13	,	,	PUNCT
ejpam-393	737	14	we	we	PRON
ejpam-393	737	15	can	can	AUX
ejpam-393	737	16	assume	assume	VERB
ejpam-393	737	17	that	that	SCONJ
ejpam-393	737	18	the	the	DET
ejpam-393	737	19	embedding	embed	VERB
ejpam-393	737	20	takes	take	VERB
ejpam-393	737	21	r	r	NOUN
ejpam-393	737	22	′	′	NOUN
ejpam-393	737	23	to	to	ADP
ejpam-393	737	24	r	r	NOUN
ejpam-393	737	25	and	and	CCONJ
ejpam-393	737	26	s′	s′	NUM
ejpam-393	737	27	to	to	ADP
ejpam-393	737	28	s.	s.	PROPN
ejpam-393	737	29	therefore	therefore	ADV
ejpam-393	737	30	n	n	PRON
ejpam-393	737	31	|=	|=	PUNCT
ejpam-393	738	1	∃	∃	PROPN
ejpam-393	738	2	x̄(χu	x̄(χu	NOUN
ejpam-393	738	3	∧	∧	NOUN
ejpam-393	738	4	x	x	INTJ
ejpam-393	738	5	(	(	PUNCT
ejpam-393	738	6	x̄	x̄	NOUN
ejpam-393	738	7	,	,	PUNCT
ejpam-393	738	8	r)∧¬x	r)∧¬x	NOUN
ejpam-393	738	9	(	(	PUNCT
ejpam-393	738	10	x̄	x̄	NOUN
ejpam-393	738	11	,	,	PUNCT
ejpam-393	738	12	s	s	PROPN
ejpam-393	738	13	)	)	PUNCT
ejpam-393	738	14	)	)	PUNCT
ejpam-393	738	15	,	,	PUNCT
ejpam-393	738	16	where	where	SCONJ
ejpam-393	738	17	x̄	x̄	PRON
ejpam-393	738	18	=	=	PUNCT
ejpam-393	738	19	〈	〈	PROPN
ejpam-393	738	20	x0	x0	PROPN
ejpam-393	738	21	,	,	PUNCT
ejpam-393	738	22	x1	x1	PROPN
ejpam-393	738	23	,	,	PUNCT
ejpam-393	738	24	x2	x2	PROPN
ejpam-393	738	25	〉	〉	NOUN
ejpam-393	738	26	.	.	PUNCT
ejpam-393	739	1	since	since	SCONJ
ejpam-393	739	2	r	r	NOUN
ejpam-393	739	3	,	,	PUNCT
ejpam-393	739	4	s	s	VERB
ejpam-393	739	5	were	be	AUX
ejpam-393	739	6	arbitrary	arbitrary	ADJ
ejpam-393	739	7	and	and	CCONJ
ejpam-393	739	8	n	n	PRON
ejpam-393	739	9	∗	∗	NOUN
ejpam-393	739	10	is	be	AUX
ejpam-393	739	11	an	an	DET
ejpam-393	739	12	elementary	elementary	ADJ
ejpam-393	739	13	extension	extension	NOUN
ejpam-393	739	14	of	of	ADP
ejpam-393	739	15	n	n	CCONJ
ejpam-393	739	16	,	,	PUNCT
ejpam-393	739	17	we	we	PRON
ejpam-393	739	18	get	get	VERB
ejpam-393	739	19	that	that	SCONJ
ejpam-393	739	20	n	n	NOUN
ejpam-393	739	21	∗	∗	NOUN
ejpam-393	739	22	|=	|=	PUNCT
ejpam-393	740	1	∀yz(p3(y)∧	∀yz(p3(y)∧	NOUN
ejpam-393	740	2	p3(z)∧	p3(z)∧	X
ejpam-393	740	3	y	y	PROPN
ejpam-393	740	4	6=	6=	PROPN
ejpam-393	740	5	z	z	NOUN
ejpam-393	740	6	−→	−→	PROPN
ejpam-393	740	7	∃	∃	PROPN
ejpam-393	740	8	x̄(χu	x̄(χu	NOUN
ejpam-393	740	9	∧	∧	NOUN
ejpam-393	740	10	x	x	INTJ
ejpam-393	740	11	(	(	PUNCT
ejpam-393	740	12	x̄	x̄	NOUN
ejpam-393	740	13	,	,	PUNCT
ejpam-393	740	14	y)∧¬(x	y)∧¬(x	NOUN
ejpam-393	740	15	(	(	PUNCT
ejpam-393	740	16	x̄	x̄	PROPN
ejpam-393	740	17	,	,	PUNCT
ejpam-393	740	18	z	z	NOUN
ejpam-393	740	19	)	)	PUNCT
ejpam-393	740	20	)	)	PUNCT
ejpam-393	740	21	)	)	PUNCT
ejpam-393	740	22	.	.	PUNCT
ejpam-393	741	1	the	the	DET
ejpam-393	741	2	result	result	NOUN
ejpam-393	741	3	for	for	SCONJ
ejpam-393	741	4	m	m	NOUN
ejpam-393	741	5	now	now	ADV
ejpam-393	741	6	follows	follow	VERB
ejpam-393	741	7	.	.	PUNCT
ejpam-393	742	1	note	note	VERB
ejpam-393	742	2	that	that	SCONJ
ejpam-393	742	3	it	it	PRON
ejpam-393	742	4	follows	follow	VERB
ejpam-393	742	5	from	from	ADP
ejpam-393	742	6	(	(	PUNCT
ejpam-393	742	7	3,4	3,4	NUM
ejpam-393	742	8	)	)	PUNCT
ejpam-393	742	9	that	that	PRON
ejpam-393	742	10	pm	pm	VERB
ejpam-393	742	11	i	i	PRON
ejpam-393	742	12	6=	6=	NUM
ejpam-393	742	13	;	;	PUNCT
ejpam-393	742	14	for	for	ADP
ejpam-393	742	15	each	each	DET
ejpam-393	742	16	i	i	PRON
ejpam-393	742	17	<	<	X
ejpam-393	742	18	3	3	X
ejpam-393	742	19	.	.	PUNCT
ejpam-393	743	1	so	so	ADV
ejpam-393	743	2	it	it	PRON
ejpam-393	743	3	is	be	AUX
ejpam-393	743	4	clear	clear	ADJ
ejpam-393	743	5	that	that	SCONJ
ejpam-393	743	6	m	m	NOUN
ejpam-393	743	7	|=	|=	VERB
ejpam-393	743	8	∀x0	∀x0	ADV
ejpam-393	743	9	x1	x1	PROPN
ejpam-393	743	10	x2(∃x	x2(∃x	PROPN
ejpam-393	743	11	iχu←→	iχu←→	ADJ
ejpam-393	743	12	∨	∨	NUM
ejpam-393	743	13	v∈33,v≡i	v∈33,v≡i	PROPN
ejpam-393	743	14	u	u	NOUN
ejpam-393	743	15	χv	χv	PROPN
ejpam-393	743	16	)	)	PUNCT
ejpam-393	743	17	;	;	PUNCT
ejpam-393	743	18	giving	give	VERB
ejpam-393	743	19	(	(	PUNCT
ejpam-393	743	20	5	5	NUM
ejpam-393	743	21	)	)	PUNCT
ejpam-393	743	22	.	.	PUNCT
ejpam-393	744	1	finally	finally	ADV
ejpam-393	744	2	consider	consider	VERB
ejpam-393	744	3	(	(	PUNCT
ejpam-393	744	4	6	6	NUM
ejpam-393	744	5	)	)	PUNCT
ejpam-393	744	6	.	.	PUNCT
ejpam-393	745	1	clearly	clearly	ADV
ejpam-393	745	2	,	,	PUNCT
ejpam-393	745	3	it	it	PRON
ejpam-393	745	4	is	be	AUX
ejpam-393	745	5	enough	enough	ADJ
ejpam-393	745	6	to	to	PART
ejpam-393	745	7	show	show	VERB
ejpam-393	745	8	that	that	SCONJ
ejpam-393	745	9	for	for	ADP
ejpam-393	745	10	any	any	DET
ejpam-393	745	11	l	l	NOUN
ejpam-393	745	12	-formula	-formula	PROPN
ejpam-393	745	13	φ	φ	X
ejpam-393	745	14	(	(	PUNCT
ejpam-393	745	15	x̄	x̄	PROPN
ejpam-393	745	16	)	)	PUNCT
ejpam-393	745	17	with	with	ADP
ejpam-393	745	18	parameters	parameter	NOUN
ejpam-393	745	19	r̄	r̄	NOUN
ejpam-393	745	20	∈	∈	PROPN
ejpam-393	745	21	pm	pm	NOUN
ejpam-393	745	22	3	3	NUM
ejpam-393	745	23	,	,	PUNCT
ejpam-393	745	24	u	u	PROPN
ejpam-393	745	25	∈	∈	PROPN
ejpam-393	745	26	s3	s3	PROPN
ejpam-393	745	27	,	,	PUNCT
ejpam-393	745	28	i	i	PRON
ejpam-393	745	29	<	<	X
ejpam-393	745	30	3	3	NUM
ejpam-393	745	31	,	,	PUNCT
ejpam-393	745	32	we	we	PRON
ejpam-393	745	33	have	have	VERB
ejpam-393	745	34	n	n	NUM
ejpam-393	745	35	|=	|=	PUNCT
ejpam-393	745	36	∃	∃	PROPN
ejpam-393	745	37	x̄(χu	x̄(χu	PROPN
ejpam-393	745	38	∧φ	∧φ	PROPN
ejpam-393	745	39	)	)	PUNCT
ejpam-393	745	40	−→∀	−→∀	PROPN
ejpam-393	745	41	x̄(∃x	x̄(∃x	VERB
ejpam-393	745	42	i(χu	i(χu	NOUN
ejpam-393	745	43	−→	−→	ADJ
ejpam-393	745	44	∃x	∃x	NOUN
ejpam-393	745	45	i(χu	i(χu	NOUN
ejpam-393	745	46	∧φ	∧φ	NOUN
ejpam-393	745	47	)	)	PUNCT
ejpam-393	745	48	)	)	PUNCT
ejpam-393	745	49	.	.	PUNCT
ejpam-393	746	1	for	for	ADP
ejpam-393	746	2	simplicity	simplicity	NOUN
ejpam-393	746	3	of	of	ADP
ejpam-393	746	4	notation	notation	NOUN
ejpam-393	746	5	assume	assume	VERB
ejpam-393	746	6	i	i	PRON
ejpam-393	746	7	=	=	NOUN
ejpam-393	747	1	2	2	X
ejpam-393	747	2	.	.	PUNCT
ejpam-393	747	3	let	let	VERB
ejpam-393	747	4	ā	ā	NOUN
ejpam-393	747	5	,	,	PUNCT
ejpam-393	747	6	b̄	b̄	VERB
ejpam-393	747	7	∈n	∈n	NOUN
ejpam-393	747	8	with	with	ADP
ejpam-393	747	9	n	n	PRON
ejpam-393	747	10	|=	|=	PUNCT
ejpam-393	747	11	(	(	PUNCT
ejpam-393	747	12	χu	χu	ADP
ejpam-393	747	13	∧φ)(ā	∧φ)(ā	NUM
ejpam-393	747	14	)	)	PUNCT
ejpam-393	747	15	and	and	CCONJ
ejpam-393	747	16	n	n	NUM
ejpam-393	747	17	|=	|=	X
ejpam-393	747	18	∃x2(χu	∃x2(χu	NOUN
ejpam-393	747	19	(	(	PUNCT
ejpam-393	747	20	b̄	b̄	NOUN
ejpam-393	747	21	)	)	PUNCT
ejpam-393	747	22	)	)	PUNCT
ejpam-393	747	23	.	.	PUNCT
ejpam-393	748	1	we	we	PRON
ejpam-393	748	2	require	require	VERB
ejpam-393	748	3	n	n	PRON
ejpam-393	748	4	|=	|=	X
ejpam-393	748	5	∃x2(χu	∃x2(χu	NOUN
ejpam-393	748	6	∧φ	∧φ	NOUN
ejpam-393	748	7	)	)	PUNCT
ejpam-393	748	8	(	(	PUNCT
ejpam-393	748	9	b̄	b̄	PROPN
ejpam-393	748	10	)	)	PUNCT
ejpam-393	748	11	.	.	PUNCT
ejpam-393	749	1	it	it	PRON
ejpam-393	749	2	follows	follow	VERB
ejpam-393	749	3	from	from	ADP
ejpam-393	749	4	the	the	DET
ejpam-393	749	5	assumptions	assumption	NOUN
ejpam-393	750	1	that	that	PRON
ejpam-393	750	2	n	n	CCONJ
ejpam-393	750	3	|=	|=	PUNCT
ejpam-393	750	4	pu0	pu0	NOUN
ejpam-393	750	5	(	(	PUNCT
ejpam-393	750	6	a0)∧	a0)∧	NOUN
ejpam-393	750	7	pu1	pu1	NOUN
ejpam-393	750	8	(	(	PUNCT
ejpam-393	750	9	a1)∧	a1)∧	PROPN
ejpam-393	750	10	a0	a0	PROPN
ejpam-393	750	11	6=	6=	SYM
ejpam-393	750	12	a1	a1	PROPN
ejpam-393	750	13	,	,	PUNCT
ejpam-393	750	14	and	and	CCONJ
ejpam-393	750	15	n	n	NUM
ejpam-393	750	16	|=	|=	PUNCT
ejpam-393	750	17	pu0	pu0	NOUN
ejpam-393	750	18	(	(	PUNCT
ejpam-393	750	19	b0)∧	b0)∧	NOUN
ejpam-393	750	20	pu1	pu1	NOUN
ejpam-393	750	21	(	(	PUNCT
ejpam-393	750	22	b1)∧	b1)∧	PROPN
ejpam-393	750	23	b0	b0	PROPN
ejpam-393	750	24	6=	6=	PROPN
ejpam-393	750	25	b1	b1	NOUN
ejpam-393	751	1	.	.	PUNCT
ejpam-393	752	1	these	these	PRON
ejpam-393	752	2	are	be	AUX
ejpam-393	752	3	the	the	DET
ejpam-393	752	4	only	only	ADJ
ejpam-393	752	5	relations	relation	NOUN
ejpam-393	752	6	on	on	ADP
ejpam-393	752	7	a0ar	a0ar	NOUN
ejpam-393	752	8	r̄	r̄	NOUN
ejpam-393	752	9	and	and	CCONJ
ejpam-393	752	10	on	on	ADP
ejpam-393	752	11	b0	b0	VERB
ejpam-393	752	12	b1	b1	NOUN
ejpam-393	752	13	r̄	r̄	NOUN
ejpam-393	752	14	(	(	PUNCT
ejpam-393	752	15	cf	cf	NOUN
ejpam-393	752	16	.	.	PUNCT
ejpam-393	753	1	property	property	NOUN
ejpam-393	753	2	(	(	PUNCT
ejpam-393	753	3	3	3	NUM
ejpam-393	753	4	)	)	PUNCT
ejpam-393	753	5	of	of	ADP
ejpam-393	753	6	lemma	lemma	PROPN
ejpam-393	753	7	13	13	NUM
ejpam-393	753	8	)	)	PUNCT
ejpam-393	753	9	,	,	PUNCT
ejpam-393	753	10	so	so	ADV
ejpam-393	753	11	θ−	θ−	PROPN
ejpam-393	753	12	=	=	SYM
ejpam-393	753	13	{	{	PUNCT
ejpam-393	753	14	(	(	PUNCT
ejpam-393	753	15	a0	a0	NOUN
ejpam-393	753	16	,	,	PUNCT
ejpam-393	753	17	b0)(a1	b0)(a1	NOUN
ejpam-393	753	18	,	,	PUNCT
ejpam-393	753	19	b1)(rl	b1)(rl	PROPN
ejpam-393	753	20	,	,	PUNCT
ejpam-393	753	21	rl	rl	PROPN
ejpam-393	753	22	)	)	PUNCT
ejpam-393	753	23	:	:	PUNCT
ejpam-393	754	1	l	l	X
ejpam-393	754	2	<	<	X
ejpam-393	754	3	|r̄|	|r̄|	PRON
ejpam-393	754	4	}	}	PUNCT
ejpam-393	754	5	is	be	AUX
ejpam-393	754	6	a	a	DET
ejpam-393	754	7	partial	partial	ADJ
ejpam-393	754	8	isomorphism	isomorphism	NOUN
ejpam-393	754	9	of	of	ADP
ejpam-393	754	10	n.	n.	NOUN
ejpam-393	754	11	by	by	ADP
ejpam-393	754	12	homogeneity	homogeneity	NOUN
ejpam-393	754	13	,	,	PUNCT
ejpam-393	754	14	it	it	PRON
ejpam-393	754	15	is	be	AUX
ejpam-393	754	16	induced	induce	VERB
ejpam-393	754	17	by	by	ADP
ejpam-393	754	18	an	an	DET
ejpam-393	754	19	automorphism	automorphism	NOUN
ejpam-393	754	20	θ	θ	PROPN
ejpam-393	754	21	of	of	ADP
ejpam-393	754	22	n.	n.	PROPN
ejpam-393	754	23	let	let	VERB
ejpam-393	754	24	c	c	NOUN
ejpam-393	754	25	=	=	SYM
ejpam-393	754	26	θ(ā	θ(ā	X
ejpam-393	754	27	)	)	PUNCT
ejpam-393	754	28	=	=	SYM
ejpam-393	754	29	(	(	PUNCT
ejpam-393	754	30	b0	b0	NOUN
ejpam-393	754	31	,	,	PUNCT
ejpam-393	754	32	b1,θ(a2	b1,θ(a2	PROPN
ejpam-393	754	33	)	)	PUNCT
ejpam-393	754	34	)	)	PUNCT
ejpam-393	754	35	.	.	PUNCT
ejpam-393	755	1	then	then	ADV
ejpam-393	755	2	n	n	X
ejpam-393	755	3	|=	|=	X
ejpam-393	755	4	(	(	PUNCT
ejpam-393	755	5	χu∧φ)(c̄	χu∧φ)(c̄	PROPN
ejpam-393	755	6	)	)	PUNCT
ejpam-393	755	7	.	.	PUNCT
ejpam-393	756	1	since	since	SCONJ
ejpam-393	756	2	c̄	c̄	PROPN
ejpam-393	756	3	≡2	≡2	NUM
ejpam-393	756	4	b̄	b̄	NOUN
ejpam-393	756	5	,	,	PUNCT
ejpam-393	756	6	we	we	PRON
ejpam-393	756	7	have	have	VERB
ejpam-393	756	8	n	n	NUM
ejpam-393	756	9	|=	|=	PUNCT
ejpam-393	756	10	∃x2(χu∧φ	∃x2(χu∧φ	NOUN
ejpam-393	756	11	)	)	PUNCT
ejpam-393	756	12	(	(	PUNCT
ejpam-393	756	13	b̄	b̄	NOUN
ejpam-393	756	14	)	)	PUNCT
ejpam-393	756	15	as	as	SCONJ
ejpam-393	756	16	required	require	VERB
ejpam-393	756	17	.	.	PUNCT
ejpam-393	757	1	now	now	ADV
ejpam-393	757	2	we	we	PRON
ejpam-393	757	3	explain	explain	VERB
ejpam-393	757	4	the	the	DET
ejpam-393	757	5	idea	idea	NOUN
ejpam-393	757	6	behind	behind	ADP
ejpam-393	757	7	the	the	DET
ejpam-393	757	8	construction	construction	NOUN
ejpam-393	757	9	of	of	ADP
ejpam-393	757	10	such	such	DET
ejpam-393	757	11	an	an	DET
ejpam-393	757	12	m	m	NOUN
ejpam-393	757	13	,	,	PUNCT
ejpam-393	757	14	and	and	CCONJ
ejpam-393	757	15	in	in	ADP
ejpam-393	757	16	the	the	DET
ejpam-393	757	17	process	process	NOUN
ejpam-393	757	18	give	give	VERB
ejpam-393	757	19	an	an	DET
ejpam-393	757	20	outline	outline	NOUN
ejpam-393	757	21	of	of	ADP
ejpam-393	757	22	the	the	DET
ejpam-393	757	23	proof	proof	NOUN
ejpam-393	757	24	that	that	SCONJ
ejpam-393	757	25	the	the	DET
ejpam-393	757	26	class	class	NOUN
ejpam-393	757	27	of	of	ADP
ejpam-393	757	28	neat	neat	ADJ
ejpam-393	757	29	reducts	reduct	NOUN
ejpam-393	757	30	is	be	AUX
ejpam-393	757	31	not	not	PART
ejpam-393	757	32	elementary	elementary	ADJ
ejpam-393	757	33	,	,	PUNCT
ejpam-393	757	34	that	that	PRON
ejpam-393	757	35	paves	pave	VERB
ejpam-393	757	36	the	the	DET
ejpam-393	757	37	way	way	NOUN
ejpam-393	757	38	for	for	ADP
ejpam-393	757	39	a	a	DET
ejpam-393	757	40	smooth	smooth	ADJ
ejpam-393	757	41	(	(	PUNCT
ejpam-393	757	42	formal	formal	ADJ
ejpam-393	757	43	)	)	PUNCT
ejpam-393	757	44	proof	proof	NOUN
ejpam-393	757	45	of	of	ADP
ejpam-393	757	46	our	our	PRON
ejpam-393	757	47	main	main	ADJ
ejpam-393	757	48	theorem	theorem	NOUN
ejpam-393	757	49	.	.	PUNCT
ejpam-393	758	1	throughout	throughout	ADP
ejpam-393	758	2	fix	fix	NOUN
ejpam-393	758	3	m	m	VERB
ejpam-393	758	4	as	as	ADP
ejpam-393	758	5	in	in	ADP
ejpam-393	758	6	lemma	lemma	PROPN
ejpam-393	758	7	9	9	NUM
ejpam-393	758	8	.	.	PUNCT
ejpam-393	759	1	t.	t.	PROPN
ejpam-393	759	2	ahmed	ahmed	PROPN
ejpam-393	759	3	/	/	SYM
ejpam-393	759	4	eur	eur	PROPN
ejpam-393	759	5	.	.	PUNCT
ejpam-393	760	1	j.	j.	PROPN
ejpam-393	760	2	pure	pure	PROPN
ejpam-393	760	3	appl	appl	PROPN
ejpam-393	760	4	.	.	PROPN
ejpam-393	760	5	math	math	PROPN
ejpam-393	760	6	,	,	PUNCT
ejpam-393	760	7	3	3	NUM
ejpam-393	760	8	(	(	PUNCT
ejpam-393	760	9	2010	2010	NUM
ejpam-393	760	10	)	)	PUNCT
ejpam-393	760	11	,	,	PUNCT
ejpam-393	760	12	853	853	NUM
ejpam-393	760	13	-	-	SYM
ejpam-393	760	14	880	880	NUM
ejpam-393	760	15	872	872	NUM
ejpam-393	760	16	we	we	PRON
ejpam-393	760	17	will	will	AUX
ejpam-393	760	18	go	go	VERB
ejpam-393	760	19	through	through	ADP
ejpam-393	760	20	the	the	DET
ejpam-393	760	21	conditions	condition	NOUN
ejpam-393	760	22	one	one	NUM
ejpam-393	760	23	by	by	ADP
ejpam-393	760	24	one	one	NUM
ejpam-393	760	25	.	.	PUNCT
ejpam-393	761	1	condition	condition	NOUN
ejpam-393	761	2	1	1	NUM
ejpam-393	761	3	of	of	ADP
ejpam-393	761	4	quantifier	quantifi	ADJ
ejpam-393	761	5	elimination	elimination	NOUN
ejpam-393	761	6	says	say	VERB
ejpam-393	761	7	that	that	SCONJ
ejpam-393	761	8	the	the	DET
ejpam-393	761	9	set	set	NOUN
ejpam-393	761	10	of	of	ADP
ejpam-393	761	11	atomic	atomic	ADJ
ejpam-393	761	12	formulas	formula	NOUN
ejpam-393	761	13	j	j	PROPN
ejpam-393	762	1	=	=	PUNCT
ejpam-393	762	2	{	{	PUNCT
ejpam-393	762	3	r(y0	r(y0	NOUN
ejpam-393	762	4	,	,	PUNCT
ejpam-393	762	5	y1	y1	NOUN
ejpam-393	762	6	,	,	PUNCT
ejpam-393	762	7	y2	y2	PROPN
ejpam-393	762	8	)	)	PUNCT
ejpam-393	762	9	:	:	PUNCT
ejpam-393	762	10	{	{	PUNCT
ejpam-393	762	11	y0	y0	NOUN
ejpam-393	762	12	,	,	PUNCT
ejpam-393	762	13	y1.y2	y1.y2	PROPN
ejpam-393	762	14	}	}	PUNCT
ejpam-393	762	15	=	=	SYM
ejpam-393	762	16	{	{	PUNCT
ejpam-393	762	17	x0	x0	PROPN
ejpam-393	762	18	,	,	PUNCT
ejpam-393	762	19	x1	x1	PROPN
ejpam-393	762	20	,	,	PUNCT
ejpam-393	762	21	x2	x2	PROPN
ejpam-393	762	22	}	}	PUNCT
ejpam-393	762	23	and	and	CCONJ
ejpam-393	762	24	r	r	NOUN
ejpam-393	762	25	∈	∈	PROPN
ejpam-393	762	26	l	l	NOUN
ejpam-393	762	27	is	be	AUX
ejpam-393	762	28	a	a	DET
ejpam-393	762	29	ternary	ternary	ADJ
ejpam-393	762	30	relation	relation	NOUN
ejpam-393	762	31	}	}	PUNCT
ejpam-393	762	32	⋃	⋃	NOUN
ejpam-393	762	33	{	{	PUNCT
ejpam-393	762	34	pi(x	pi(x	NOUN
ejpam-393	762	35	j	j	PROPN
ejpam-393	762	36	)	)	PUNCT
ejpam-393	762	37	:	:	PUNCT
ejpam-393	763	1	i	i	PRON
ejpam-393	763	2	,	,	PUNCT
ejpam-393	763	3	j	j	PROPN
ejpam-393	763	4	<	<	X
ejpam-393	763	5	3	3	NUM
ejpam-393	763	6	}	}	PUNCT
ejpam-393	763	7	∪	∪	NOUN
ejpam-393	763	8	{	{	PUNCT
ejpam-393	763	9	x	x	NOUN
ejpam-393	763	10	i	i	NOUN
ejpam-393	763	11	=	=	PUNCT
ejpam-393	763	12	x	x	PUNCT
ejpam-393	763	13	j	j	NOUN
ejpam-393	763	14	:	:	PUNCT
ejpam-393	763	15	i	i	PROPN
ejpam-393	763	16	,	,	PUNCT
ejpam-393	763	17	j	j	PROPN
ejpam-393	763	18	<	<	X
ejpam-393	763	19	3	3	NUM
ejpam-393	763	20	}	}	PUNCT
ejpam-393	763	21	is	be	AUX
ejpam-393	763	22	an	an	DET
ejpam-393	763	23	elimination	elimination	NOUN
ejpam-393	763	24	set	set	NOUN
ejpam-393	763	25	for	for	ADP
ejpam-393	763	26	m	m	PRON
ejpam-393	763	27	,	,	PUNCT
ejpam-393	763	28	meaning	mean	VERB
ejpam-393	763	29	that	that	SCONJ
ejpam-393	763	30	every	every	DET
ejpam-393	763	31	formula	formula	NOUN
ejpam-393	763	32	φ	φ	PROPN
ejpam-393	763	33	∈	∈	PROPN
ejpam-393	763	34	l	l	NOUN
ejpam-393	763	35	is	be	AUX
ejpam-393	763	36	equivalent	equivalent	ADJ
ejpam-393	763	37	in	in	ADP
ejpam-393	763	38	m	m	PROPN
ejpam-393	763	39	to	to	ADP
ejpam-393	763	40	a	a	DET
ejpam-393	763	41	boolean	boolean	ADJ
ejpam-393	763	42	combination	combination	NOUN
ejpam-393	763	43	of	of	ADP
ejpam-393	763	44	formulas	formula	NOUN
ejpam-393	763	45	in	in	ADP
ejpam-393	763	46	j	j	PROPN
ejpam-393	763	47	.	.	PUNCT
ejpam-393	764	1	this	this	PRON
ejpam-393	764	2	implies	imply	VERB
ejpam-393	764	3	that	that	SCONJ
ejpam-393	764	4	the	the	DET
ejpam-393	764	5	cylindric	cylindric	ADJ
ejpam-393	764	6	set	set	NOUN
ejpam-393	764	7	algebra	algebra	NOUN
ejpam-393	764	8	based	base	VERB
ejpam-393	764	9	on	on	ADP
ejpam-393	764	10	m	m	AUX
ejpam-393	764	11	using	use	VERB
ejpam-393	764	12	only	only	ADV
ejpam-393	764	13	the	the	DET
ejpam-393	764	14	first	first	ADJ
ejpam-393	764	15	three	three	NUM
ejpam-393	764	16	variables	variable	NOUN
ejpam-393	764	17	is	be	AUX
ejpam-393	764	18	a	a	DET
ejpam-393	764	19	neat	neat	ADJ
ejpam-393	764	20	reduct	reduct	NOUN
ejpam-393	764	21	.	.	PUNCT
ejpam-393	765	1	in	in	ADP
ejpam-393	765	2	more	more	ADJ
ejpam-393	765	3	detail	detail	NOUN
ejpam-393	765	4	,	,	PUNCT
ejpam-393	765	5	for	for	ADP
ejpam-393	765	6	φ	φ	PROPN
ejpam-393	765	7	∈	∈	PROPN
ejpam-393	765	8	l	l	NOUN
ejpam-393	765	9	,	,	PUNCT
ejpam-393	765	10	let	let	VERB
ejpam-393	765	11	φm	φm	PART
ejpam-393	765	12	be	be	AUX
ejpam-393	765	13	the	the	DET
ejpam-393	765	14	set	set	NOUN
ejpam-393	765	15	of	of	ADP
ejpam-393	765	16	all	all	DET
ejpam-393	765	17	assignments	assignment	NOUN
ejpam-393	765	18	satisfying	satisfy	VERB
ejpam-393	765	19	φ	φ	PROPN
ejpam-393	765	20	in	in	ADP
ejpam-393	765	21	m	m	PROPN
ejpam-393	765	22	i.e.	i.e.	X
ejpam-393	765	23	φm	φm	X
ejpam-393	765	24	=	=	PUNCT
ejpam-393	765	25	{	{	PUNCT
ejpam-393	765	26	s	s	NOUN
ejpam-393	765	27	∈	∈	NOUN
ejpam-393	765	28	ωm	ωm	NUM
ejpam-393	765	29	:	:	PUNCT
ejpam-393	765	30	m	m	NUM
ejpam-393	765	31	|=	|=	VERB
ejpam-393	765	32	φ[s	φ[s	PROPN
ejpam-393	765	33	]	]	PUNCT
ejpam-393	765	34	}	}	PUNCT
ejpam-393	765	35	.	.	PUNCT
ejpam-393	766	1	csn	csn	PROPN
ejpam-393	766	2	denotes	denote	VERB
ejpam-393	766	3	the	the	DET
ejpam-393	766	4	class	class	NOUN
ejpam-393	766	5	of	of	ADP
ejpam-393	766	6	cylindric	cylindric	ADJ
ejpam-393	766	7	set	set	NOUN
ejpam-393	766	8	algebras	algebra	NOUN
ejpam-393	766	9	of	of	ADP
ejpam-393	766	10	dimension	dimension	NOUN
ejpam-393	766	11	n.	n.	PROPN
ejpam-393	766	12	let	let	VERB
ejpam-393	766	13	aω	aω	PART
ejpam-393	766	14	be	be	AUX
ejpam-393	766	15	the	the	DET
ejpam-393	766	16	csω	csω	NOUN
ejpam-393	766	17	with	with	ADP
ejpam-393	766	18	domain	domain	NOUN
ejpam-393	766	19	{	{	PUNCT
ejpam-393	766	20	φm	φm	PROPN
ejpam-393	766	21	:	:	PUNCT
ejpam-393	766	22	φ	φ	PROPN
ejpam-393	766	23	∈	∈	PROPN
ejpam-393	766	24	l	l	NOUN
ejpam-393	766	25	}	}	PUNCT
ejpam-393	766	26	and	and	CCONJ
ejpam-393	766	27	operations	operation	NOUN
ejpam-393	766	28	(	(	PUNCT
ejpam-393	766	29	well-	well-	X
ejpam-393	766	30	)	)	PUNCT
ejpam-393	766	31	defined	define	VERB
ejpam-393	766	32	by	by	ADP
ejpam-393	766	33	(	(	PUNCT
ejpam-393	766	34	cf.[12])†	cf.[12])†	NOUN
ejpam-393	766	35	φm.ψm	φm.ψm	PROPN
ejpam-393	766	36	=	=	PRON
ejpam-393	766	37	φm	φm	VERB
ejpam-393	766	38	∩ψm	∩ψm	ADV
ejpam-393	766	39	=	=	SYM
ejpam-393	766	40	(	(	PUNCT
ejpam-393	766	41	φ	φ	PROPN
ejpam-393	766	42	∧ψ)m	∧ψ)m	PROPN
ejpam-393	766	43	;	;	PUNCT
ejpam-393	766	44	−φm	−φm	PROPN
ejpam-393	766	45	=	=	SYM
ejpam-393	766	46	(	(	PUNCT
ejpam-393	766	47	¬φ)m	¬φ)m	ADP
ejpam-393	766	48	;	;	PUNCT
ejpam-393	766	49	and	and	CCONJ
ejpam-393	766	50	for	for	ADP
ejpam-393	766	51	i	i	PRON
ejpam-393	766	52	,	,	PUNCT
ejpam-393	766	53	j	j	PROPN
ejpam-393	766	54	<	<	X
ejpam-393	766	55	ω	ω	X
ejpam-393	766	56	di	di	X
ejpam-393	766	57	j	j	PROPN
ejpam-393	766	58	=	=	PUNCT
ejpam-393	766	59	(	(	PUNCT
ejpam-393	766	60	x	x	X
ejpam-393	766	61	i	i	NOUN
ejpam-393	766	62	=	=	NOUN
ejpam-393	766	63	x	x	SYM
ejpam-393	766	64	j	j	PROPN
ejpam-393	766	65	)	)	PUNCT
ejpam-393	766	66	m	m	PROPN
ejpam-393	766	67	;	;	PUNCT
ejpam-393	766	68	and	and	CCONJ
ejpam-393	766	69	ci(φ	ci(φ	NUM
ejpam-393	766	70	m	m	NOUN
ejpam-393	766	71	)	)	PUNCT
ejpam-393	766	72	=	=	SYM
ejpam-393	767	1	(	(	PUNCT
ejpam-393	767	2	∃x	∃x	PROPN
ejpam-393	767	3	iφ	iφ	NOUN
ejpam-393	767	4	)	)	PUNCT
ejpam-393	767	5	m.	m.	NOUN
ejpam-393	767	6	now	now	ADV
ejpam-393	767	7	write	write	VERB
ejpam-393	767	8	l3	l3	NOUN
ejpam-393	767	9	for	for	ADP
ejpam-393	767	10	the	the	DET
ejpam-393	767	11	set	set	NOUN
ejpam-393	767	12	of	of	ADP
ejpam-393	767	13	all	all	DET
ejpam-393	767	14	l	l	NOUN
ejpam-393	767	15	-	-	NOUN
ejpam-393	767	16	formulas	formula	NOUN
ejpam-393	767	17	using	use	VERB
ejpam-393	767	18	only	only	ADV
ejpam-393	767	19	the	the	DET
ejpam-393	767	20	first	first	ADJ
ejpam-393	767	21	three	three	NUM
ejpam-393	767	22	variables	variable	NOUN
ejpam-393	767	23	.	.	PUNCT
ejpam-393	768	1	then	then	ADV
ejpam-393	768	2	a	a	DET
ejpam-393	768	3	moment	moment	NOUN
ejpam-393	768	4	’s	’s	PART
ejpam-393	768	5	reflection	reflection	NOUN
ejpam-393	768	6	will	will	AUX
ejpam-393	768	7	show	show	VERB
ejpam-393	768	8	that	that	SCONJ
ejpam-393	768	9	condition	condition	NOUN
ejpam-393	768	10	1	1	NUM
ejpam-393	768	11	says	say	VERB
ejpam-393	768	12	that	that	SCONJ
ejpam-393	768	13	the	the	DET
ejpam-393	768	14	cs3	cs3	PROPN
ejpam-393	768	15	a	a	PRON
ejpam-393	768	16	with	with	ADP
ejpam-393	768	17	domain	domain	NOUN
ejpam-393	768	18	{	{	PUNCT
ejpam-393	768	19	φm	φm	PROPN
ejpam-393	768	20	:	:	PUNCT
ejpam-393	768	21	φ	φ	PROPN
ejpam-393	768	22	∈	∈	PROPN
ejpam-393	768	23	l3	l3	NOUN
ejpam-393	768	24	}	}	PUNCT
ejpam-393	768	25	is	be	AUX
ejpam-393	768	26	the	the	DET
ejpam-393	768	27	same	same	ADJ
ejpam-393	768	28	as	as	ADP
ejpam-393	768	29	the	the	DET
ejpam-393	768	30	(	(	PUNCT
ejpam-393	768	31	possibly	possibly	ADV
ejpam-393	768	32	bigger	big	ADJ
ejpam-393	768	33	)	)	PUNCT
ejpam-393	768	34	cs3	cs3	PROPN
ejpam-393	768	35	with	with	ADP
ejpam-393	768	36	domain	domain	NOUN
ejpam-393	768	37	{	{	PUNCT
ejpam-393	768	38	φm	φm	PROPN
ejpam-393	768	39	:	:	PUNCT
ejpam-393	768	40	φ	φ	PROPN
ejpam-393	768	41	∈	∈	PROPN
ejpam-393	768	42	l	l	NOUN
ejpam-393	768	43	and	and	CCONJ
ejpam-393	768	44	φ	φ	PROPN
ejpam-393	768	45	contains	contain	VERB
ejpam-393	768	46	x0	x0	PROPN
ejpam-393	768	47	,	,	PUNCT
ejpam-393	768	48	x1	x1	PROPN
ejpam-393	768	49	,	,	PUNCT
ejpam-393	769	1	x2	x2	PROPN
ejpam-393	769	2	as	as	ADP
ejpam-393	769	3	free	free	ADJ
ejpam-393	769	4	variables	variable	NOUN
ejpam-393	769	5	}	}	PUNCT
ejpam-393	769	6	,	,	PUNCT
ejpam-393	769	7	with	with	SCONJ
ejpam-393	769	8	the	the	DET
ejpam-393	769	9	operation	operation	NOUN
ejpam-393	769	10	defined	define	VERB
ejpam-393	769	11	,	,	PUNCT
ejpam-393	769	12	for	for	ADP
ejpam-393	769	13	both	both	PRON
ejpam-393	769	14	,	,	PUNCT
ejpam-393	769	15	as	as	ADP
ejpam-393	769	16	for	for	ADP
ejpam-393	769	17	aω	aω	PROPN
ejpam-393	769	18	.	.	PUNCT
ejpam-393	770	1	but	but	CCONJ
ejpam-393	770	2	the	the	DET
ejpam-393	770	3	latter	latter	ADJ
ejpam-393	770	4	,	,	PUNCT
ejpam-393	770	5	as	as	SCONJ
ejpam-393	770	6	easily	easily	ADV
ejpam-393	770	7	checked	check	VERB
ejpam-393	770	8	,	,	PUNCT
ejpam-393	770	9	is	be	AUX
ejpam-393	770	10	isomorphic	isomorphic	ADJ
ejpam-393	770	11	to	to	ADP
ejpam-393	770	12	nr3aω	nr3aω	NUM
ejpam-393	770	13	,	,	PUNCT
ejpam-393	770	14	so	so	ADV
ejpam-393	770	15	condition	condition	NOUN
ejpam-393	770	16	1	1	NUM
ejpam-393	770	17	guarantees	guarantee	VERB
ejpam-393	770	18	that	that	SCONJ
ejpam-393	770	19	a	a	DET
ejpam-393	770	20	∈nr3caω	∈nr3caω	PROPN
ejpam-393	770	21	.	.	PUNCT
ejpam-393	771	1	the	the	DET
ejpam-393	771	2	rest	rest	NOUN
ejpam-393	771	3	of	of	ADP
ejpam-393	771	4	the	the	DET
ejpam-393	771	5	conditions	condition	NOUN
ejpam-393	771	6	are	be	AUX
ejpam-393	771	7	designed	design	VERB
ejpam-393	771	8	to	to	PART
ejpam-393	771	9	extract	extract	VERB
ejpam-393	771	10	an	an	DET
ejpam-393	771	11	elementary	elementary	ADJ
ejpam-393	771	12	subalgebra	subalgebra	NOUN
ejpam-393	771	13	of	of	ADP
ejpam-393	771	14	a	a	DET
ejpam-393	771	15	such	such	ADJ
ejpam-393	771	16	that	that	SCONJ
ejpam-393	771	17	its	its	PRON
ejpam-393	771	18	rsc	rsc	PROPN
ejpam-393	771	19	reduct	reduct	PROPN
ejpam-393	771	20	is	be	AUX
ejpam-393	771	21	not	not	PART
ejpam-393	771	22	in	in	ADP
ejpam-393	771	23	nr3(rsc5	nr3(rsc5	NUM
ejpam-393	771	24	)	)	PUNCT
ejpam-393	771	25	.	.	PUNCT
ejpam-393	772	1	but	but	CCONJ
ejpam-393	772	2	let	let	VERB
ejpam-393	772	3	us	we	PRON
ejpam-393	772	4	first	first	ADV
ejpam-393	772	5	understand	understand	VERB
ejpam-393	772	6	the	the	DET
ejpam-393	772	7	(	(	PUNCT
ejpam-393	772	8	abstract	abstract	ADJ
ejpam-393	772	9	)	)	PUNCT
ejpam-393	772	10	structure	structure	NOUN
ejpam-393	772	11	of	of	ADP
ejpam-393	772	12	a	a	PRON
ejpam-393	772	13	based	base	VERB
ejpam-393	772	14	on	on	ADP
ejpam-393	772	15	m.	m.	NOUN
ejpam-393	772	16	condition	condition	NOUN
ejpam-393	772	17	(	(	PUNCT
ejpam-393	772	18	2	2	NUM
ejpam-393	772	19	)	)	PUNCT
ejpam-393	772	20	,	,	PUNCT
ejpam-393	772	21	says	say	VERB
ejpam-393	772	22	that	that	SCONJ
ejpam-393	772	23	{	{	PUNCT
ejpam-393	772	24	χm	χm	NUM
ejpam-393	772	25	u	u	NOUN
ejpam-393	772	26	:	:	PUNCT
ejpam-393	772	27	u	u	NOUN
ejpam-393	772	28	∈	∈	PROPN
ejpam-393	772	29	33	33	NUM
ejpam-393	772	30	}	}	PUNCT
ejpam-393	772	31	†in	†in	NOUN
ejpam-393	773	1	[	[	X
ejpam-393	773	2	12	12	NUM
ejpam-393	773	3	]	]	PUNCT
ejpam-393	773	4	,	,	PUNCT
ejpam-393	773	5	sec	sec	PROPN
ejpam-393	773	6	4.3	4.3	NUM
ejpam-393	773	7	,	,	PUNCT
ejpam-393	773	8	cf	cf	NOUN
ejpam-393	773	9	.	.	PUNCT
ejpam-393	774	1	definition	definition	NOUN
ejpam-393	774	2	4.3.4	4.3.4	NUM
ejpam-393	774	3	aω	aω	NOUN
ejpam-393	774	4	would	would	AUX
ejpam-393	774	5	be	be	AUX
ejpam-393	774	6	denoted	denote	VERB
ejpam-393	774	7	by	by	ADP
ejpam-393	774	8	c	c	PROPN
ejpam-393	774	9	f	f	PROPN
ejpam-393	774	10	m	m	VERB
ejpam-393	774	11	3	3	NUM
ejpam-393	774	12	,	,	PUNCT
ejpam-393	774	13	which	which	PRON
ejpam-393	774	14	is	be	AUX
ejpam-393	774	15	the	the	DET
ejpam-393	774	16	set	set	ADJ
ejpam-393	774	17	algebra	algebra	NOUN
ejpam-393	774	18	based	base	VERB
ejpam-393	774	19	on	on	ADP
ejpam-393	774	20	m.	m.	NOUN
ejpam-393	774	21	in	in	ADP
ejpam-393	774	22	this	this	DET
ejpam-393	774	23	connection	connection	NOUN
ejpam-393	774	24	we	we	PRON
ejpam-393	774	25	note	note	VERB
ejpam-393	774	26	that	that	SCONJ
ejpam-393	774	27	a	a	PRON
ejpam-393	774	28	is	be	AUX
ejpam-393	774	29	a	a	DET
ejpam-393	774	30	regular	regular	ADJ
ejpam-393	774	31	locally	locally	ADV
ejpam-393	774	32	finite	finite	ADJ
ejpam-393	774	33	csω	csω	NOUN
ejpam-393	774	34	.	.	PUNCT
ejpam-393	775	1	t.	t.	PROPN
ejpam-393	775	2	ahmed	ahmed	PROPN
ejpam-393	775	3	/	/	SYM
ejpam-393	775	4	eur	eur	PROPN
ejpam-393	775	5	.	.	PUNCT
ejpam-393	776	1	j.	j.	PROPN
ejpam-393	776	2	pure	pure	PROPN
ejpam-393	776	3	appl	appl	PROPN
ejpam-393	776	4	.	.	PROPN
ejpam-393	776	5	math	math	PROPN
ejpam-393	776	6	,	,	PUNCT
ejpam-393	776	7	3	3	NUM
ejpam-393	776	8	(	(	PUNCT
ejpam-393	776	9	2010	2010	NUM
ejpam-393	776	10	)	)	PUNCT
ejpam-393	776	11	,	,	PUNCT
ejpam-393	776	12	853	853	NUM
ejpam-393	776	13	-	-	SYM
ejpam-393	776	14	880	880	NUM
ejpam-393	776	15	873	873	NUM
ejpam-393	776	16	is	be	AUX
ejpam-393	776	17	a	a	DET
ejpam-393	776	18	partition	partition	NOUN
ejpam-393	776	19	of	of	ADP
ejpam-393	776	20	3	3	NUM
ejpam-393	776	21	m	m	NOUN
ejpam-393	776	22	,	,	PUNCT
ejpam-393	776	23	the	the	DET
ejpam-393	776	24	unit	unit	NOUN
ejpam-393	776	25	of	of	ADP
ejpam-393	776	26	a.	a.	NOUN
ejpam-393	776	27	that	that	PRON
ejpam-393	776	28	is	be	AUX
ejpam-393	776	29	⋃	⋃	PROPN
ejpam-393	776	30	u∈33	u∈33	PROPN
ejpam-393	776	31	(	(	PUNCT
ejpam-393	776	32	χu	χu	NOUN
ejpam-393	776	33	)	)	PUNCT
ejpam-393	776	34	m	m	VERB
ejpam-393	776	35	=	=	PUNCT
ejpam-393	776	36	3	3	NUM
ejpam-393	776	37	m	m	NOUN
ejpam-393	776	38	,	,	PUNCT
ejpam-393	776	39	and	and	CCONJ
ejpam-393	776	40	for	for	ADP
ejpam-393	776	41	distinct	distinct	ADJ
ejpam-393	776	42	u	u	NOUN
ejpam-393	776	43	,	,	PUNCT
ejpam-393	776	44	v	v	PROPN
ejpam-393	776	45	∈	∈	PROPN
ejpam-393	776	46	33	33	NUM
ejpam-393	776	47	we	we	PRON
ejpam-393	776	48	have	have	VERB
ejpam-393	776	49	(	(	PUNCT
ejpam-393	776	50	χu	χu	NOUN
ejpam-393	776	51	)	)	PUNCT
ejpam-393	776	52	m	m	PROPN
ejpam-393	776	53	∩	∩	NOUN
ejpam-393	776	54	(	(	PUNCT
ejpam-393	776	55	χv	χv	NOUN
ejpam-393	776	56	)	)	PUNCT
ejpam-393	776	57	m	m	PROPN
ejpam-393	776	58	=	=	PUNCT
ejpam-393	776	59	;	;	PUNCT
ejpam-393	776	60	.	.	PUNCT
ejpam-393	777	1	conditions	condition	NOUN
ejpam-393	777	2	(	(	PUNCT
ejpam-393	777	3	3	3	NUM
ejpam-393	777	4	)	)	PUNCT
ejpam-393	777	5	and	and	CCONJ
ejpam-393	777	6	(	(	PUNCT
ejpam-393	777	7	4	4	X
ejpam-393	777	8	)	)	PUNCT
ejpam-393	777	9	single	single	ADJ
ejpam-393	777	10	out	out	ADP
ejpam-393	777	11	the	the	DET
ejpam-393	777	12	χm	χm	PROPN
ejpam-393	777	13	u	u	PROPN
ejpam-393	777	14	’s	’s	NOUN
ejpam-393	777	15	that	that	PRON
ejpam-393	777	16	are	be	AUX
ejpam-393	777	17	indexed	index	VERB
ejpam-393	777	18	by	by	ADP
ejpam-393	777	19	permutations	permutation	NOUN
ejpam-393	777	20	u	u	PROPN
ejpam-393	777	21	∈	∈	PROPN
ejpam-393	777	22	s3	s3	PROPN
ejpam-393	777	23	.	.	PUNCT
ejpam-393	777	24	note	note	VERB
ejpam-393	777	25	that	that	SCONJ
ejpam-393	777	26	for	for	ADP
ejpam-393	777	27	any	any	DET
ejpam-393	777	28	such	such	ADJ
ejpam-393	777	29	u	u	NOUN
ejpam-393	777	30	,	,	PUNCT
ejpam-393	777	31	if	if	SCONJ
ejpam-393	777	32	〈	〈	PROPN
ejpam-393	777	33	a0	a0	PROPN
ejpam-393	777	34	,	,	PUNCT
ejpam-393	777	35	a1	a1	NOUN
ejpam-393	777	36	,	,	PUNCT
ejpam-393	777	37	a2	a2	NOUN
ejpam-393	777	38	〉	〉	NOUN
ejpam-393	777	39	∈	∈	PROPN
ejpam-393	777	40	χ	χ	NOUN
ejpam-393	777	41	m	m	VERB
ejpam-393	777	42	u	u	NOUN
ejpam-393	777	43	,	,	PUNCT
ejpam-393	777	44	then	then	ADV
ejpam-393	777	45	the	the	DET
ejpam-393	777	46	ai	ai	NOUN
ejpam-393	777	47	’s	’s	ADV
ejpam-393	777	48	are	be	AUX
ejpam-393	777	49	distinct	distinct	ADJ
ejpam-393	777	50	because	because	SCONJ
ejpam-393	777	51	ai	ai	VERB
ejpam-393	777	52	∈	∈	PROPN
ejpam-393	777	53	pui	pui	PROPN
ejpam-393	777	54	for	for	ADP
ejpam-393	777	55	i	i	PRON
ejpam-393	777	56	<	<	X
ejpam-393	777	57	3	3	NUM
ejpam-393	777	58	and	and	CCONJ
ejpam-393	777	59	by	by	ADP
ejpam-393	777	60	(	(	PUNCT
ejpam-393	777	61	2	2	X
ejpam-393	777	62	)	)	PUNCT
ejpam-393	777	63	these	these	PRON
ejpam-393	777	64	are	be	AUX
ejpam-393	777	65	disjoint	disjoint	ADJ
ejpam-393	777	66	.	.	PUNCT
ejpam-393	778	1	condition	condition	NOUN
ejpam-393	778	2	(	(	PUNCT
ejpam-393	778	3	3	3	X
ejpam-393	778	4	)	)	PUNCT
ejpam-393	778	5	says	say	VERB
ejpam-393	778	6	that	that	SCONJ
ejpam-393	778	7	for	for	ADP
ejpam-393	778	8	any	any	DET
ejpam-393	778	9	ternary	ternary	ADJ
ejpam-393	778	10	r	r	NOUN
ejpam-393	778	11	(	(	PUNCT
ejpam-393	778	12	x̄	x̄	NOUN
ejpam-393	778	13	)	)	PUNCT
ejpam-393	778	14	∈	∈	PROPN
ejpam-393	778	15	l	l	NOUN
ejpam-393	778	16	,	,	PUNCT
ejpam-393	778	17	r	r	X
ejpam-393	778	18	(	(	PUNCT
ejpam-393	778	19	x̄)m	x̄)m	NOUN
ejpam-393	778	20	⊆	⊆	NUM
ejpam-393	778	21	⋃	⋃	PROPN
ejpam-393	778	22	u∈s3	u∈s3	NOUN
ejpam-393	778	23	(	(	PUNCT
ejpam-393	778	24	χu	χu	NOUN
ejpam-393	778	25	)	)	PUNCT
ejpam-393	778	26	m	m	VERB
ejpam-393	778	27	with	with	ADP
ejpam-393	778	28	u	u	PROPN
ejpam-393	778	29	∈	∈	PROPN
ejpam-393	778	30	s3	s3	PROPN
ejpam-393	778	31	,	,	PUNCT
ejpam-393	778	32	so	so	SCONJ
ejpam-393	778	33	this	this	PRON
ejpam-393	778	34	means	mean	VERB
ejpam-393	778	35	that	that	SCONJ
ejpam-393	778	36	if	if	SCONJ
ejpam-393	778	37	〈	〈	PROPN
ejpam-393	778	38	a0	a0	NOUN
ejpam-393	778	39	,	,	PUNCT
ejpam-393	778	40	a1	a1	NOUN
ejpam-393	778	41	,	,	PUNCT
ejpam-393	778	42	a2	a2	NOUN
ejpam-393	778	43	〉	〉	NOUN
ejpam-393	778	44	∈	∈	PROPN
ejpam-393	778	45	r	r	PROPN
ejpam-393	778	46	(	(	PUNCT
ejpam-393	778	47	x̄)m	x̄)m	PROPN
ejpam-393	778	48	,	,	PUNCT
ejpam-393	778	49	then	then	ADV
ejpam-393	778	50	the	the	DET
ejpam-393	778	51	ai	ai	NOUN
ejpam-393	778	52	’s	’	VERB
ejpam-393	778	53	must	must	AUX
ejpam-393	778	54	be	be	AUX
ejpam-393	778	55	distinct	distinct	ADJ
ejpam-393	778	56	,	,	PUNCT
ejpam-393	778	57	too	too	ADV
ejpam-393	778	58	.	.	PUNCT
ejpam-393	779	1	condition	condition	NOUN
ejpam-393	779	2	(	(	PUNCT
ejpam-393	779	3	4	4	NUM
ejpam-393	779	4	)	)	PUNCT
ejpam-393	779	5	says	say	VERB
ejpam-393	779	6	that	that	SCONJ
ejpam-393	779	7	below	below	ADP
ejpam-393	779	8	every	every	DET
ejpam-393	779	9	such	such	ADJ
ejpam-393	779	10	(	(	PUNCT
ejpam-393	779	11	χu	χu	NOUN
ejpam-393	779	12	)	)	PUNCT
ejpam-393	779	13	m	m	AUX
ejpam-393	779	14	with	with	ADP
ejpam-393	779	15	u	u	PROPN
ejpam-393	779	16	∈	∈	PROPN
ejpam-393	779	17	s3	s3	PROPN
ejpam-393	779	18	,	,	PUNCT
ejpam-393	779	19	there	there	PRON
ejpam-393	779	20	are	be	VERB
ejpam-393	779	21	uncountably	uncountably	ADV
ejpam-393	779	22	many	many	ADJ
ejpam-393	779	23	pairwise	pairwise	NOUN
ejpam-393	779	24	distinct	distinct	ADJ
ejpam-393	779	25	non	non	ADJ
ejpam-393	779	26	-	-	ADJ
ejpam-393	779	27	empty	empty	ADJ
ejpam-393	779	28	elements	element	NOUN
ejpam-393	779	29	,	,	PUNCT
ejpam-393	779	30	namely	namely	ADV
ejpam-393	779	31	,	,	PUNCT
ejpam-393	779	32	the	the	DET
ejpam-393	779	33	r	r	NOUN
ejpam-393	779	34	(	(	PUNCT
ejpam-393	779	35	x̄)m∩(χu	x̄)m∩(χu	PROPN
ejpam-393	779	36	)	)	PUNCT
ejpam-393	779	37	m	m	PROPN
ejpam-393	779	38	,	,	PUNCT
ejpam-393	779	39	for	for	ADP
ejpam-393	779	40	ternary	ternary	ADJ
ejpam-393	779	41	r	r	NOUN
ejpam-393	779	42	∈	∈	PROPN
ejpam-393	779	43	l.	l.	NOUN
ejpam-393	779	44	condition	condition	NOUN
ejpam-393	779	45	(	(	PUNCT
ejpam-393	779	46	5	5	X
ejpam-393	779	47	)	)	PUNCT
ejpam-393	779	48	tells	tell	VERB
ejpam-393	779	49	us	we	PRON
ejpam-393	779	50	how	how	SCONJ
ejpam-393	779	51	the	the	DET
ejpam-393	779	52	(	(	PUNCT
ejpam-393	779	53	χu	χu	NOUN
ejpam-393	779	54	)	)	PUNCT
ejpam-393	779	55	m	m	VERB
ejpam-393	779	56	’s	’s	NOUN
ejpam-393	779	57	behave	behave	VERB
ejpam-393	779	58	with	with	ADP
ejpam-393	779	59	respect	respect	NOUN
ejpam-393	779	60	to	to	ADP
ejpam-393	779	61	cylindrifications	cylindrification	NOUN
ejpam-393	779	62	.	.	PUNCT
ejpam-393	780	1	it	it	PRON
ejpam-393	780	2	simply	simply	ADV
ejpam-393	780	3	says	say	VERB
ejpam-393	780	4	that	that	SCONJ
ejpam-393	780	5	for	for	ADP
ejpam-393	780	6	u	u	PROPN
ejpam-393	780	7	∈	∈	PROPN
ejpam-393	780	8	s3	s3	PROPN
ejpam-393	780	9	and	and	CCONJ
ejpam-393	780	10	i	i	PRON
ejpam-393	780	11	<	<	X
ejpam-393	780	12	3	3	NUM
ejpam-393	780	13	we	we	PRON
ejpam-393	780	14	have	have	VERB
ejpam-393	780	15	ci(χu	ci(χu	NOUN
ejpam-393	780	16	)	)	PUNCT
ejpam-393	780	17	m	m	PROPN
ejpam-393	780	18	=	=	PUNCT
ejpam-393	780	19	⋃	⋃	PROPN
ejpam-393	780	20	v∈33,v≡iu	v∈33,v≡iu	X
ejpam-393	780	21	(	(	PUNCT
ejpam-393	780	22	χv	χv	NOUN
ejpam-393	780	23	)	)	PUNCT
ejpam-393	780	24	m.	m.	NOUN
ejpam-393	780	25	a	a	DET
ejpam-393	780	26	moment	moment	NOUN
ejpam-393	780	27	’s	’s	PART
ejpam-393	780	28	reflection	reflection	NOUN
ejpam-393	780	29	will	will	AUX
ejpam-393	780	30	reveal	reveal	VERB
ejpam-393	780	31	that	that	SCONJ
ejpam-393	780	32	this	this	PRON
ejpam-393	780	33	follows	follow	VERB
ejpam-393	780	34	from	from	ADP
ejpam-393	780	35	(	(	PUNCT
ejpam-393	780	36	3	3	NUM
ejpam-393	780	37	)	)	PUNCT
ejpam-393	780	38	and	and	CCONJ
ejpam-393	780	39	(	(	PUNCT
ejpam-393	780	40	4	4	NUM
ejpam-393	780	41	.	.	PUNCT
ejpam-393	780	42	)	)	PUNCT
ejpam-393	780	43	finally	finally	ADV
ejpam-393	780	44	,	,	PUNCT
ejpam-393	780	45	condition	condition	NOUN
ejpam-393	780	46	(	(	PUNCT
ejpam-393	780	47	6	6	NUM
ejpam-393	780	48	)	)	PUNCT
ejpam-393	780	49	says	say	VERB
ejpam-393	780	50	that	that	SCONJ
ejpam-393	780	51	elements	element	NOUN
ejpam-393	780	52	below	below	ADP
ejpam-393	780	53	χm	χm	NOUN
ejpam-393	780	54	u	u	NOUN
ejpam-393	780	55	are	be	AUX
ejpam-393	780	56	big	big	ADJ
ejpam-393	780	57	,	,	PUNCT
ejpam-393	780	58	as	as	ADV
ejpam-393	780	59	far	far	ADV
ejpam-393	780	60	as	as	SCONJ
ejpam-393	780	61	cylindrifications	cylindrification	NOUN
ejpam-393	780	62	are	be	AUX
ejpam-393	780	63	concerned	concern	VERB
ejpam-393	780	64	,	,	PUNCT
ejpam-393	780	65	that	that	PRON
ejpam-393	780	66	is	be	AUX
ejpam-393	780	67	for	for	ADP
ejpam-393	780	68	any	any	DET
ejpam-393	780	69	φ	φ	NOUN
ejpam-393	780	70	such	such	ADJ
ejpam-393	780	71	that	that	SCONJ
ejpam-393	780	72	(	(	PUNCT
ejpam-393	780	73	φ	φ	PROPN
ejpam-393	780	74	∩	∩	PROPN
ejpam-393	780	75	χu	χu	PART
ejpam-393	780	76	)	)	PUNCT
ejpam-393	780	77	m	m	PROPN
ejpam-393	780	78	6=	6=	NUM
ejpam-393	780	79	;	;	PUNCT
ejpam-393	780	80	and	and	CCONJ
ejpam-393	780	81	any	any	DET
ejpam-393	780	82	i	i	PRON
ejpam-393	780	83	<	<	X
ejpam-393	780	84	3	3	NUM
ejpam-393	780	85	,	,	PUNCT
ejpam-393	780	86	we	we	PRON
ejpam-393	780	87	have	have	VERB
ejpam-393	780	88	ci(φ	ci(φ	NUM
ejpam-393	780	89	m	m	VERB
ejpam-393	780	90	∩χm	∩χm	NOUN
ejpam-393	780	91	u	u	NOUN
ejpam-393	780	92	)	)	PUNCT
ejpam-393	781	1	=	=	SYM
ejpam-393	781	2	ci(χ	ci(χ	NOUN
ejpam-393	781	3	m	m	VERB
ejpam-393	781	4	u	u	NOUN
ejpam-393	781	5	)	)	PUNCT
ejpam-393	781	6	=	=	SYM
ejpam-393	781	7	⋃	⋃	PROPN
ejpam-393	781	8	v∈33,v≡iu	v∈33,v≡iu	X
ejpam-393	781	9	(	(	PUNCT
ejpam-393	781	10	χv	χv	NOUN
ejpam-393	781	11	)	)	PUNCT
ejpam-393	781	12	m.	m.	NOUN
ejpam-393	781	13	summarizing	summarize	VERB
ejpam-393	781	14	the	the	DET
ejpam-393	781	15	above	above	NOUN
ejpam-393	781	16	,	,	PUNCT
ejpam-393	781	17	let	let	VERB
ejpam-393	781	18	1u	1u	PRON
ejpam-393	781	19	denote	denote	VERB
ejpam-393	781	20	χm	χm	PROPN
ejpam-393	781	21	u	u	PROPN
ejpam-393	781	22	.	.	PUNCT
ejpam-393	782	1	then	then	ADV
ejpam-393	782	2	by	by	ADP
ejpam-393	782	3	condition	condition	NOUN
ejpam-393	782	4	(	(	PUNCT
ejpam-393	782	5	2	2	NUM
ejpam-393	782	6	)	)	PUNCT
ejpam-393	782	7	,	,	PUNCT
ejpam-393	782	8	we	we	PRON
ejpam-393	782	9	have	have	VERB
ejpam-393	782	10	{	{	PUNCT
ejpam-393	782	11	1u	1u	NOUN
ejpam-393	782	12	:	:	PUNCT
ejpam-393	782	13	u	u	NOUN
ejpam-393	782	14	∈	∈	NOUN
ejpam-393	782	15	33	33	NUM
ejpam-393	782	16	}	}	PUNCT
ejpam-393	782	17	is	be	AUX
ejpam-393	782	18	a	a	DET
ejpam-393	782	19	partition	partition	NOUN
ejpam-393	782	20	of	of	ADP
ejpam-393	782	21	the	the	DET
ejpam-393	782	22	unit	unit	NOUN
ejpam-393	782	23	of	of	ADP
ejpam-393	782	24	a.	a.	NOUN
ejpam-393	782	25	if	if	SCONJ
ejpam-393	782	26	u	u	PROPN
ejpam-393	782	27	∈	∈	PROPN
ejpam-393	782	28	s3	s3	PROPN
ejpam-393	782	29	,	,	PUNCT
ejpam-393	782	30	then	then	ADV
ejpam-393	782	31	below	below	ADP
ejpam-393	782	32	every	every	DET
ejpam-393	782	33	1u	1u	NUM
ejpam-393	782	34	,	,	PUNCT
ejpam-393	782	35	there	there	PRON
ejpam-393	782	36	are	be	VERB
ejpam-393	782	37	uncountably	uncountably	ADV
ejpam-393	782	38	many	many	ADJ
ejpam-393	782	39	pairwise	pairwise	NOUN
ejpam-393	782	40	distinct	distinct	ADJ
ejpam-393	782	41	non	non	ADJ
ejpam-393	782	42	empty	empty	ADJ
ejpam-393	782	43	elements	element	NOUN
ejpam-393	782	44	,	,	PUNCT
ejpam-393	782	45	namely	namely	ADV
ejpam-393	782	46	the	the	DET
ejpam-393	782	47	r	r	NOUN
ejpam-393	782	48	(	(	PUNCT
ejpam-393	782	49	x̄)m	x̄)m	PROPN
ejpam-393	782	50	’s	’s	ADV
ejpam-393	782	51	intersected	intersect	VERB
ejpam-393	782	52	with	with	ADP
ejpam-393	782	53	1u	1u	NUM
ejpam-393	782	54	.	.	PUNCT
ejpam-393	783	1	(	(	PUNCT
ejpam-393	783	2	conditions	condition	NOUN
ejpam-393	783	3	(	(	PUNCT
ejpam-393	783	4	3	3	NUM
ejpam-393	783	5	)	)	PUNCT
ejpam-393	783	6	,	,	PUNCT
ejpam-393	783	7	(	(	PUNCT
ejpam-393	783	8	4	4	NUM
ejpam-393	783	9	)	)	PUNCT
ejpam-393	783	10	)	)	PUNCT
ejpam-393	783	11	.	.	PUNCT
ejpam-393	784	1	such	such	ADJ
ejpam-393	784	2	elements	element	NOUN
ejpam-393	784	3	are	be	AUX
ejpam-393	784	4	big	big	ADJ
ejpam-393	784	5	as	as	ADV
ejpam-393	784	6	far	far	ADV
ejpam-393	784	7	as	as	SCONJ
ejpam-393	784	8	the	the	DET
ejpam-393	784	9	cylindrifications	cylindrification	NOUN
ejpam-393	784	10	are	be	AUX
ejpam-393	784	11	concerned	concern	VERB
ejpam-393	784	12	,	,	PUNCT
ejpam-393	784	13	that	that	PRON
ejpam-393	784	14	is	be	AUX
ejpam-393	784	15	for	for	ADP
ejpam-393	784	16	i	i	PRON
ejpam-393	784	17	<	<	X
ejpam-393	784	18	3	3	NUM
ejpam-393	784	19	we	we	PRON
ejpam-393	784	20	have	have	VERB
ejpam-393	784	21	(	(	PUNCT
ejpam-393	784	22	by	by	ADP
ejpam-393	784	23	conditions	condition	NOUN
ejpam-393	784	24	(	(	PUNCT
ejpam-393	784	25	5	5	NUM
ejpam-393	784	26	)	)	PUNCT
ejpam-393	784	27	,	,	PUNCT
ejpam-393	784	28	(	(	PUNCT
ejpam-393	784	29	6	6	NUM
ejpam-393	784	30	)	)	PUNCT
ejpam-393	784	31	)	)	PUNCT
ejpam-393	784	32	ci(r	ci(r	NOUN
ejpam-393	785	1	(	(	PUNCT
ejpam-393	785	2	x̄	x̄	PROPN
ejpam-393	785	3	)	)	PUNCT
ejpam-393	785	4	m	m	VERB
ejpam-393	785	5	∩	∩	NOUN
ejpam-393	785	6	1u	1u	NUM
ejpam-393	785	7	)	)	PUNCT
ejpam-393	785	8	=	=	SYM
ejpam-393	785	9	ci(1u	ci(1u	NOUN
ejpam-393	785	10	)	)	PUNCT
ejpam-393	785	11	=	=	PUNCT
ejpam-393	786	1	⋃	⋃	ADP
ejpam-393	786	2	v≡iu	v≡iu	PROPN
ejpam-393	786	3	1u	1u	NUM
ejpam-393	786	4	.	.	PUNCT
ejpam-393	787	1	having	having	AUX
ejpam-393	787	2	explained	explain	VERB
ejpam-393	787	3	the	the	DET
ejpam-393	787	4	idea	idea	NOUN
ejpam-393	787	5	behind	behind	ADP
ejpam-393	787	6	the	the	DET
ejpam-393	787	7	conditions	condition	NOUN
ejpam-393	787	8	of	of	ADP
ejpam-393	787	9	lemma	lemma	PROPN
ejpam-393	787	10	13	13	NUM
ejpam-393	787	11	we	we	PRON
ejpam-393	787	12	explain	explain	VERB
ejpam-393	787	13	how	how	SCONJ
ejpam-393	787	14	we	we	PRON
ejpam-393	787	15	will	will	AUX
ejpam-393	787	16	go	go	VERB
ejpam-393	787	17	about	about	ADP
ejpam-393	787	18	extracting	extract	VERB
ejpam-393	787	19	an	an	DET
ejpam-393	787	20	elementary	elementary	ADJ
ejpam-393	787	21	subalgebra	subalgebra	NOUN
ejpam-393	787	22	of	of	ADP
ejpam-393	787	23	a	a	PRON
ejpam-393	787	24	that	that	PRON
ejpam-393	787	25	is	be	AUX
ejpam-393	787	26	not	not	PART
ejpam-393	787	27	a	a	DET
ejpam-393	787	28	neat	neat	ADJ
ejpam-393	787	29	reduct	reduct	NOUN
ejpam-393	787	30	.	.	PUNCT
ejpam-393	788	1	for	for	ADP
ejpam-393	788	2	u	u	PROPN
ejpam-393	788	3	∈	∈	PROPN
ejpam-393	788	4	33	33	NUM
ejpam-393	788	5	,	,	PUNCT
ejpam-393	788	6	let	let	VERB
ejpam-393	788	7	au	au	ADV
ejpam-393	788	8	stand	stand	VERB
ejpam-393	788	9	for	for	ADP
ejpam-393	788	10	the	the	DET
ejpam-393	788	11	relativisation	relativisation	NOUN
ejpam-393	788	12	of	of	ADP
ejpam-393	788	13	a	a	PRON
ejpam-393	788	14	to	to	ADP
ejpam-393	788	15	1u	1u	PRON
ejpam-393	788	16	i.e.	i.e.	X
ejpam-393	788	17	au	au	X
ejpam-393	788	18	=	=	PUNCT
ejpam-393	788	19	{	{	PUNCT
ejpam-393	788	20	x	x	PUNCT
ejpam-393	788	21	∈	∈	PROPN
ejpam-393	788	22	a	a	DET
ejpam-393	788	23	:	:	PUNCT
ejpam-393	788	24	x	x	SYM
ejpam-393	788	25	≤	≤	ADJ
ejpam-393	788	26	1u	1u	NUM
ejpam-393	788	27	}	}	PUNCT
ejpam-393	788	28	.	.	PUNCT
ejpam-393	789	1	au	au	PROPN
ejpam-393	789	2	is	be	AUX
ejpam-393	789	3	the	the	DET
ejpam-393	789	4	domain	domain	NOUN
ejpam-393	789	5	of	of	ADP
ejpam-393	789	6	a	a	DET
ejpam-393	789	7	boolean	boolean	ADJ
ejpam-393	789	8	set	set	NOUN
ejpam-393	789	9	algebra	algebra	NOUN
ejpam-393	789	10	which	which	PRON
ejpam-393	789	11	we	we	PRON
ejpam-393	789	12	denote	denote	VERB
ejpam-393	789	13	by	by	ADP
ejpam-393	789	14	au	au	PROPN
ejpam-393	789	15	.	.	PROPN
ejpam-393	789	16	then	then	ADV
ejpam-393	789	17	for	for	ADP
ejpam-393	789	18	u	u	PROPN
ejpam-393	789	19	∈	∈	PROPN
ejpam-393	789	20	s3	s3	PROPN
ejpam-393	789	21	,	,	PUNCT
ejpam-393	789	22	au	au	X
ejpam-393	789	23	is	be	AUX
ejpam-393	789	24	uncountable	uncountable	ADJ
ejpam-393	789	25	.	.	PUNCT
ejpam-393	790	1	because	because	SCONJ
ejpam-393	790	2	{	{	PUNCT
ejpam-393	790	3	1u	1u	NOUN
ejpam-393	790	4	:	:	PUNCT
ejpam-393	790	5	u	u	NOUN
ejpam-393	790	6	∈	∈	NOUN
ejpam-393	790	7	33	33	NUM
ejpam-393	790	8	}	}	PUNCT
ejpam-393	790	9	is	be	AUX
ejpam-393	790	10	a	a	DET
ejpam-393	790	11	partition	partition	NOUN
ejpam-393	790	12	of	of	ADP
ejpam-393	790	13	the	the	DET
ejpam-393	790	14	unit	unit	NOUN
ejpam-393	790	15	of	of	ADP
ejpam-393	790	16	a	a	PRON
ejpam-393	790	17	,	,	PUNCT
ejpam-393	790	18	it	it	PRON
ejpam-393	790	19	follows	follow	VERB
ejpam-393	790	20	that	that	SCONJ
ejpam-393	790	21	the	the	DET
ejpam-393	790	22	boolean	boolean	ADJ
ejpam-393	790	23	t.	t.	PROPN
ejpam-393	790	24	ahmed	ahmed	PROPN
ejpam-393	790	25	/	/	SYM
ejpam-393	790	26	eur	eur	PROPN
ejpam-393	790	27	.	.	PUNCT
ejpam-393	791	1	j.	j.	PROPN
ejpam-393	791	2	pure	pure	PROPN
ejpam-393	791	3	appl	appl	PROPN
ejpam-393	791	4	.	.	PROPN
ejpam-393	791	5	math	math	PROPN
ejpam-393	791	6	,	,	PUNCT
ejpam-393	791	7	3	3	NUM
ejpam-393	791	8	(	(	PUNCT
ejpam-393	791	9	2010	2010	NUM
ejpam-393	791	10	)	)	PUNCT
ejpam-393	791	11	,	,	PUNCT
ejpam-393	791	12	853	853	NUM
ejpam-393	791	13	-	-	SYM
ejpam-393	791	14	880	880	NUM
ejpam-393	791	15	874	874	NUM
ejpam-393	791	16	reduct	reduct	NOUN
ejpam-393	791	17	of	of	ADP
ejpam-393	791	18	a	a	PRON
ejpam-393	791	19	is	be	AUX
ejpam-393	791	20	isomorphic	isomorphic	ADJ
ejpam-393	791	21	to	to	ADP
ejpam-393	791	22	the	the	DET
ejpam-393	791	23	boolean	boolean	ADJ
ejpam-393	791	24	product	product	NOUN
ejpam-393	791	25	,	,	PUNCT
ejpam-393	791	26	∏	∏	PROPN
ejpam-393	791	27	u∈33	u∈33	X
ejpam-393	791	28	au	au	PROPN
ejpam-393	791	29	.	.	PUNCT
ejpam-393	792	1	moreover	moreover	ADV
ejpam-393	792	2	we	we	PRON
ejpam-393	792	3	can	can	AUX
ejpam-393	792	4	expand	expand	VERB
ejpam-393	792	5	the	the	DET
ejpam-393	792	6	language	language	NOUN
ejpam-393	792	7	of	of	ADP
ejpam-393	792	8	boolean	boolean	ADJ
ejpam-393	792	9	algebras	algebra	NOUN
ejpam-393	792	10	by	by	ADP
ejpam-393	792	11	diagonal	diagonal	ADJ
ejpam-393	792	12	elements	element	NOUN
ejpam-393	792	13	and	and	CCONJ
ejpam-393	792	14	the	the	DET
ejpam-393	792	15	constants	constant	NOUN
ejpam-393	792	16	1u	1u	NUM
ejpam-393	792	17	in	in	ADP
ejpam-393	792	18	such	such	DET
ejpam-393	792	19	a	a	DET
ejpam-393	792	20	way	way	NOUN
ejpam-393	792	21	that	that	PRON
ejpam-393	792	22	the	the	DET
ejpam-393	792	23	cylindric	cylindric	ADJ
ejpam-393	792	24	algebra	algebra	NOUN
ejpam-393	792	25	a	a	PRON
ejpam-393	792	26	becomes	become	VERB
ejpam-393	792	27	interpretable	interpretable	ADJ
ejpam-393	792	28	in	in	ADP
ejpam-393	792	29	this	this	DET
ejpam-393	792	30	product	product	NOUN
ejpam-393	792	31	.	.	PUNCT
ejpam-393	793	1	then	then	ADV
ejpam-393	793	2	we	we	PRON
ejpam-393	793	3	are	be	AUX
ejpam-393	793	4	able	able	ADJ
ejpam-393	793	5	to	to	PART
ejpam-393	793	6	extract	extract	VERB
ejpam-393	793	7	an	an	DET
ejpam-393	793	8	elementary	elementary	ADJ
ejpam-393	793	9	subalgebra	subalgebra	PROPN
ejpam-393	793	10	b	b	PROPN
ejpam-393	793	11	of	of	ADP
ejpam-393	793	12	a	a	PRON
ejpam-393	793	13	by	by	ADP
ejpam-393	793	14	an	an	DET
ejpam-393	793	15	infinite	infinite	ADJ
ejpam-393	793	16	cardinality	cardinality	NOUN
ejpam-393	793	17	twist	twist	NOUN
ejpam-393	793	18	,	,	PUNCT
ejpam-393	793	19	that	that	SCONJ
ejpam-393	793	20	first	first	ADJ
ejpam-393	793	21	order	order	NOUN
ejpam-393	793	22	logic	logic	NOUN
ejpam-393	793	23	does	do	AUX
ejpam-393	793	24	not	not	PART
ejpam-393	793	25	see	see	VERB
ejpam-393	793	26	.	.	PUNCT
ejpam-393	794	1	b	b	NOUN
ejpam-393	794	2	is	be	AUX
ejpam-393	794	3	simply	simply	ADV
ejpam-393	794	4	obtained	obtain	VERB
ejpam-393	794	5	from	from	ADP
ejpam-393	794	6	a	a	PRON
ejpam-393	794	7	by	by	ADP
ejpam-393	794	8	keeping	keep	VERB
ejpam-393	794	9	only	only	ADV
ejpam-393	794	10	many	many	ADJ
ejpam-393	794	11	countably	countably	ADJ
ejpam-393	794	12	elements	element	NOUN
ejpam-393	794	13	below	below	ADP
ejpam-393	794	14	1i	1i	NOUN
ejpam-393	794	15	d	d	NOUN
ejpam-393	794	16	,	,	PUNCT
ejpam-393	794	17	where	where	SCONJ
ejpam-393	794	18	i	i	PRON
ejpam-393	794	19	d	d	PROPN
ejpam-393	794	20	is	be	AUX
ejpam-393	794	21	the	the	DET
ejpam-393	794	22	identity	identity	NOUN
ejpam-393	794	23	function	function	NOUN
ejpam-393	794	24	on	on	ADP
ejpam-393	794	25	3	3	NUM
ejpam-393	794	26	,	,	PUNCT
ejpam-393	794	27	and	and	CCONJ
ejpam-393	794	28	throwing	throw	VERB
ejpam-393	794	29	away	away	ADP
ejpam-393	794	30	the	the	DET
ejpam-393	794	31	rest	rest	NOUN
ejpam-393	794	32	of	of	ADP
ejpam-393	794	33	the	the	DET
ejpam-393	794	34	elements	element	NOUN
ejpam-393	794	35	below	below	ADP
ejpam-393	794	36	1i	1i	NOUN
ejpam-393	794	37	d	d	NOUN
ejpam-393	794	38	.	.	PUNCT
ejpam-393	795	1	in	in	ADP
ejpam-393	795	2	the	the	DET
ejpam-393	795	3	product	product	NOUN
ejpam-393	795	4	,	,	PUNCT
ejpam-393	795	5	this	this	PRON
ejpam-393	795	6	corresponds	correspond	VERB
ejpam-393	795	7	to	to	ADP
ejpam-393	795	8	replacing	replace	VERB
ejpam-393	795	9	the	the	DET
ejpam-393	795	10	component	component	NOUN
ejpam-393	795	11	ai	ai	VERB
ejpam-393	795	12	d	d	NOUN
ejpam-393	795	13	by	by	ADP
ejpam-393	795	14	an	an	DET
ejpam-393	795	15	arbitrary	arbitrary	ADJ
ejpam-393	795	16	elementary	elementary	ADJ
ejpam-393	795	17	countable	countable	ADJ
ejpam-393	795	18	boolean	boolean	ADJ
ejpam-393	795	19	subalgebra	subalgebra	NOUN
ejpam-393	795	20	bi	bi	PROPN
ejpam-393	795	21	d	d	PROPN
ejpam-393	795	22	of	of	ADP
ejpam-393	795	23	ai	ai	PROPN
ejpam-393	795	24	d	d	PROPN
ejpam-393	795	25	and	and	CCONJ
ejpam-393	795	26	giving	give	VERB
ejpam-393	795	27	the	the	DET
ejpam-393	795	28	resulting	result	VERB
ejpam-393	795	29	algebra	algebra	NOUN
ejpam-393	795	30	the	the	DET
ejpam-393	795	31	interpretation	interpretation	NOUN
ejpam-393	795	32	given	give	VERB
ejpam-393	795	33	to	to	ADP
ejpam-393	795	34	the	the	DET
ejpam-393	795	35	the	the	DET
ejpam-393	795	36	boolean	boolean	ADJ
ejpam-393	795	37	product	product	NOUN
ejpam-393	795	38	∏	∏	PROPN
ejpam-393	795	39	u∈33	u∈33	X
ejpam-393	795	40	au	au	PROPN
ejpam-393	795	41	.	.	PUNCT
ejpam-393	796	1	this	this	PRON
ejpam-393	796	2	will	will	AUX
ejpam-393	796	3	not	not	PART
ejpam-393	796	4	be	be	AUX
ejpam-393	796	5	witnessed	witness	VERB
ejpam-393	796	6	by	by	ADP
ejpam-393	796	7	first	first	ADJ
ejpam-393	796	8	order	order	NOUN
ejpam-393	796	9	logic	logic	NOUN
ejpam-393	796	10	,	,	PUNCT
ejpam-393	796	11	but	but	CCONJ
ejpam-393	796	12	will	will	AUX
ejpam-393	796	13	enforce	enforce	VERB
ejpam-393	796	14	that	that	SCONJ
ejpam-393	796	15	the	the	DET
ejpam-393	796	16	resulting	result	VERB
ejpam-393	796	17	structure	structure	NOUN
ejpam-393	796	18	b	b	NOUN
ejpam-393	796	19	,	,	PUNCT
ejpam-393	796	20	which	which	PRON
ejpam-393	796	21	is	be	AUX
ejpam-393	796	22	of	of	ADP
ejpam-393	796	23	course	course	NOUN
ejpam-393	796	24	a	a	DET
ejpam-393	796	25	ca3	ca3	NOUN
ejpam-393	796	26	,	,	PUNCT
ejpam-393	796	27	is	be	AUX
ejpam-393	796	28	not	not	PART
ejpam-393	796	29	a	a	DET
ejpam-393	796	30	neat	neat	ADJ
ejpam-393	796	31	reduct	reduct	NOUN
ejpam-393	796	32	.	.	PUNCT
ejpam-393	797	1	in	in	ADP
ejpam-393	797	2	fact	fact	NOUN
ejpam-393	797	3	,	,	PUNCT
ejpam-393	797	4	b	b	NOUN
ejpam-393	797	5	will	will	AUX
ejpam-393	797	6	not	not	PART
ejpam-393	797	7	be	be	AUX
ejpam-393	797	8	even	even	ADV
ejpam-393	797	9	in	in	ADP
ejpam-393	797	10	nr3ca4	nr3ca4	NOUN
ejpam-393	797	11	and	and	CCONJ
ejpam-393	797	12	its	its	PRON
ejpam-393	797	13	rsc	rsc	PROPN
ejpam-393	797	14	reduct	reduct	PROPN
ejpam-393	797	15	is	be	AUX
ejpam-393	797	16	not	not	PART
ejpam-393	797	17	in	in	ADP
ejpam-393	797	18	nr3rsc5	nr3rsc5	PROPN
ejpam-393	797	19	.	.	PUNCT
ejpam-393	798	1	the	the	DET
ejpam-393	798	2	idea	idea	NOUN
ejpam-393	798	3	is	be	AUX
ejpam-393	798	4	that	that	PRON
ejpam-393	798	5	had	have	VERB
ejpam-393	798	6	b	b	NOUN
ejpam-393	798	7	been	be	AUX
ejpam-393	798	8	a	a	DET
ejpam-393	798	9	neat	neat	ADJ
ejpam-393	798	10	reduct	reduct	NOUN
ejpam-393	798	11	then	then	ADV
ejpam-393	798	12	using	use	VERB
ejpam-393	798	13	a	a	DET
ejpam-393	798	14	substitution	substitution	NOUN
ejpam-393	798	15	term	term	NOUN
ejpam-393	798	16	definable	definable	ADJ
ejpam-393	798	17	in	in	ADP
ejpam-393	798	18	extra	extra	ADJ
ejpam-393	798	19	dimensions	dimension	NOUN
ejpam-393	798	20	,	,	PUNCT
ejpam-393	798	21	will	will	AUX
ejpam-393	798	22	give	give	VERB
ejpam-393	798	23	uncountably	uncountably	ADV
ejpam-393	798	24	many	many	ADJ
ejpam-393	798	25	elements	element	NOUN
ejpam-393	798	26	in	in	ADP
ejpam-393	798	27	the	the	DET
ejpam-393	798	28	component	component	NOUN
ejpam-393	798	29	bi	bi	PROPN
ejpam-393	798	30	d	d	PROPN
ejpam-393	798	31	,	,	PUNCT
ejpam-393	798	32	which	which	PRON
ejpam-393	798	33	contradicts	contradict	VERB
ejpam-393	798	34	that	that	SCONJ
ejpam-393	798	35	the	the	DET
ejpam-393	798	36	latter	latter	ADJ
ejpam-393	798	37	,	,	PUNCT
ejpam-393	798	38	by	by	ADP
ejpam-393	798	39	construction	construction	NOUN
ejpam-393	798	40	,	,	PUNCT
ejpam-393	798	41	is	be	AUX
ejpam-393	798	42	countable	countable	ADJ
ejpam-393	798	43	.	.	PUNCT
ejpam-393	799	1	now	now	ADV
ejpam-393	799	2	we	we	PRON
ejpam-393	799	3	implement	implement	VERB
ejpam-393	799	4	the	the	DET
ejpam-393	799	5	details	detail	NOUN
ejpam-393	799	6	of	of	ADP
ejpam-393	799	7	the	the	DET
ejpam-393	799	8	above	above	ADJ
ejpam-393	799	9	sketch	sketch	NOUN
ejpam-393	799	10	.	.	PUNCT
ejpam-393	800	1	proof	proof	NOUN
ejpam-393	800	2	.	.	PUNCT
ejpam-393	801	1	[	[	X
ejpam-393	801	2	main	main	ADJ
ejpam-393	801	3	result	result	NOUN
ejpam-393	801	4	]	]	PUNCT
ejpam-393	801	5	fix	fix	NOUN
ejpam-393	801	6	l	l	NOUN
ejpam-393	801	7	and	and	CCONJ
ejpam-393	801	8	m	m	NOUN
ejpam-393	801	9	as	as	ADP
ejpam-393	801	10	in	in	ADP
ejpam-393	801	11	lemma	lemma	PROPN
ejpam-393	801	12	9	9	NUM
ejpam-393	801	13	.	.	PUNCT
ejpam-393	802	1	let	let	VERB
ejpam-393	802	2	aω	aω	VERB
ejpam-393	802	3	,	,	PUNCT
ejpam-393	802	4	a	a	DET
ejpam-393	802	5	be	be	AUX
ejpam-393	802	6	as	as	ADV
ejpam-393	802	7	specified	specify	VERB
ejpam-393	802	8	above	above	ADV
ejpam-393	802	9	.	.	PUNCT
ejpam-393	803	1	that	that	PRON
ejpam-393	803	2	is	be	AUX
ejpam-393	803	3	aω	aω	PROPN
ejpam-393	803	4	=	=	PUNCT
ejpam-393	803	5	{	{	PUNCT
ejpam-393	803	6	φ	φ	PROPN
ejpam-393	803	7	m	m	VERB
ejpam-393	803	8	:	:	PUNCT
ejpam-393	803	9	φ	φ	PROPN
ejpam-393	803	10	∈	∈	PROPN
ejpam-393	803	11	l	l	NOUN
ejpam-393	803	12	}	}	PUNCT
ejpam-393	803	13	and	and	CCONJ
ejpam-393	803	14	a=	a=	VERB
ejpam-393	803	15	{	{	PUNCT
ejpam-393	803	16	φm	φm	X
ejpam-393	803	17	:	:	PUNCT
ejpam-393	803	18	φ	φ	PROPN
ejpam-393	803	19	∈	∈	PROPN
ejpam-393	803	20	l3	l3	PROPN
ejpam-393	803	21	}	}	PUNCT
ejpam-393	803	22	.	.	PUNCT
ejpam-393	804	1	then	then	ADV
ejpam-393	804	2	a∼=nr3aω	a∼=nr3aω	ADJ
ejpam-393	804	3	,	,	PUNCT
ejpam-393	804	4	the	the	DET
ejpam-393	804	5	isomorphism	isomorphism	NOUN
ejpam-393	804	6	is	be	AUX
ejpam-393	804	7	given	give	VERB
ejpam-393	804	8	by	by	ADP
ejpam-393	804	9	φm	φm	ADP
ejpam-393	804	10	7→	7→	PROPN
ejpam-393	804	11	φm	φm	NOUN
ejpam-393	804	12	.	.	NOUN
ejpam-393	804	13	quantifier	quantifier	VERB
ejpam-393	804	14	elimination	elimination	NOUN
ejpam-393	804	15	in	in	ADP
ejpam-393	804	16	m	m	NOUN
ejpam-393	804	17	guarantees	guarantee	NOUN
ejpam-393	804	18	that	that	SCONJ
ejpam-393	804	19	this	this	DET
ejpam-393	804	20	map	map	NOUN
ejpam-393	804	21	is	be	AUX
ejpam-393	804	22	onto	onto	ADP
ejpam-393	804	23	.	.	PUNCT
ejpam-393	805	1	for	for	ADP
ejpam-393	805	2	u	u	PROPN
ejpam-393	805	3	∈	∈	PROPN
ejpam-393	805	4	33	33	NUM
ejpam-393	805	5	,	,	PUNCT
ejpam-393	805	6	let	let	VERB
ejpam-393	805	7	au	au	VERB
ejpam-393	805	8	denote	denote	VERB
ejpam-393	805	9	the	the	DET
ejpam-393	805	10	relativisation	relativisation	NOUN
ejpam-393	805	11	of	of	ADP
ejpam-393	805	12	a	a	DET
ejpam-393	805	13	to	to	PART
ejpam-393	805	14	χm	χm	VERB
ejpam-393	805	15	u	u	NOUN
ejpam-393	805	16	i.e	i.e	X
ejpam-393	805	17	au	au	ADV
ejpam-393	805	18	=	=	PUNCT
ejpam-393	805	19	{	{	PUNCT
ejpam-393	805	20	x	x	PUNCT
ejpam-393	805	21	∈	∈	PROPN
ejpam-393	805	22	a	a	DET
ejpam-393	805	23	:	:	PUNCT
ejpam-393	805	24	x	x	SYM
ejpam-393	805	25	≤	≤	PROPN
ejpam-393	805	26	χm	χm	NUM
ejpam-393	805	27	u	u	NOUN
ejpam-393	805	28	}	}	PUNCT
ejpam-393	805	29	.	.	PUNCT
ejpam-393	806	1	au	au	PROPN
ejpam-393	806	2	is	be	AUX
ejpam-393	806	3	a	a	DET
ejpam-393	806	4	boolean	boolean	ADJ
ejpam-393	806	5	algebra	algebra	NOUN
ejpam-393	806	6	.	.	PUNCT
ejpam-393	807	1	also	also	ADV
ejpam-393	807	2	au	au	VERB
ejpam-393	807	3	is	be	AUX
ejpam-393	807	4	uncountable	uncountable	ADJ
ejpam-393	807	5	for	for	ADP
ejpam-393	807	6	every	every	DET
ejpam-393	807	7	u	u	PROPN
ejpam-393	807	8	∈	∈	PROPN
ejpam-393	807	9	s3	s3	PROPN
ejpam-393	807	10	because	because	SCONJ
ejpam-393	807	11	by	by	ADP
ejpam-393	807	12	property	property	NOUN
ejpam-393	807	13	(	(	PUNCT
ejpam-393	807	14	4	4	NUM
ejpam-393	807	15	)	)	PUNCT
ejpam-393	807	16	of	of	ADP
ejpam-393	807	17	lemma	lemma	PROPN
ejpam-393	807	18	9	9	NUM
ejpam-393	807	19	the	the	DET
ejpam-393	807	20	sets	set	NOUN
ejpam-393	807	21	(	(	PUNCT
ejpam-393	807	22	χu	χu	ADP
ejpam-393	807	23	∧	∧	PROPN
ejpam-393	807	24	r(x0	r(x0	NOUN
ejpam-393	807	25	,	,	PUNCT
ejpam-393	807	26	x1	x1	PROPN
ejpam-393	807	27	,	,	PUNCT
ejpam-393	807	28	x2	x2	PROPN
ejpam-393	807	29	)	)	PUNCT
ejpam-393	807	30	)	)	PUNCT
ejpam-393	808	1	m	m	PROPN
ejpam-393	808	2	,	,	PUNCT
ejpam-393	808	3	for	for	ADP
ejpam-393	808	4	r	r	NOUN
ejpam-393	808	5	∈	∈	PROPN
ejpam-393	808	6	l	l	NOUN
ejpam-393	808	7	are	be	AUX
ejpam-393	808	8	distinct	distinct	ADJ
ejpam-393	808	9	elements	element	NOUN
ejpam-393	808	10	of	of	ADP
ejpam-393	808	11	au	au	PROPN
ejpam-393	808	12	.	.	PROPN
ejpam-393	808	13	define	define	VERB
ejpam-393	808	14	a	a	DET
ejpam-393	808	15	map	map	NOUN
ejpam-393	808	16	f	f	X
ejpam-393	808	17	:	:	PUNCT
ejpam-393	808	18	a→	a→	PUNCT
ejpam-393	808	19	∏	∏	PROPN
ejpam-393	808	20	u∈33(au	u∈33(au	PROPN
ejpam-393	808	21	)	)	PUNCT
ejpam-393	808	22	,	,	PUNCT
ejpam-393	808	23	by	by	ADP
ejpam-393	808	24	f	f	PROPN
ejpam-393	808	25	(	(	PUNCT
ejpam-393	808	26	a	a	NOUN
ejpam-393	808	27	)	)	PUNCT
ejpam-393	808	28	=	=	SYM
ejpam-393	809	1	〈	〈	PROPN
ejpam-393	809	2	a.χu〉u∈33	a.χu〉u∈33	PROPN
ejpam-393	809	3	.	.	PUNCT
ejpam-393	810	1	we	we	PRON
ejpam-393	810	2	will	will	AUX
ejpam-393	810	3	expand	expand	VERB
ejpam-393	810	4	the	the	DET
ejpam-393	810	5	language	language	NOUN
ejpam-393	810	6	of	of	ADP
ejpam-393	810	7	the	the	DET
ejpam-393	810	8	boolean	boolean	ADJ
ejpam-393	810	9	algebra	algebra	NOUN
ejpam-393	810	10	∏	∏	PROPN
ejpam-393	810	11	u∈33	u∈33	X
ejpam-393	810	12	au	au	NOUN
ejpam-393	810	13	in	in	ADP
ejpam-393	810	14	such	such	DET
ejpam-393	810	15	a	a	DET
ejpam-393	810	16	way	way	NOUN
ejpam-393	810	17	that	that	PRON
ejpam-393	810	18	the	the	DET
ejpam-393	810	19	cylindric	cylindric	ADJ
ejpam-393	810	20	algebra	algebra	NOUN
ejpam-393	810	21	a	a	PRON
ejpam-393	810	22	becomes	become	VERB
ejpam-393	810	23	interpretable	interpretable	ADJ
ejpam-393	810	24	in	in	ADP
ejpam-393	810	25	the	the	DET
ejpam-393	810	26	expanded	expand	VERB
ejpam-393	810	27	structure	structure	NOUN
ejpam-393	810	28	.	.	PUNCT
ejpam-393	811	1	for	for	ADP
ejpam-393	811	2	this	this	PRON
ejpam-393	811	3	we	we	PRON
ejpam-393	811	4	need	need	VERB
ejpam-393	811	5	.	.	PUNCT
ejpam-393	812	1	definition	definition	NOUN
ejpam-393	812	2	10	10	NUM
ejpam-393	812	3	.	.	PUNCT
ejpam-393	813	1	let	let	VERB
ejpam-393	813	2	¶	¶	PROPN
ejpam-393	813	3	denote	denote	VERB
ejpam-393	813	4	the	the	DET
ejpam-393	813	5	following	follow	VERB
ejpam-393	813	6	structure	structure	NOUN
ejpam-393	813	7	for	for	ADP
ejpam-393	813	8	the	the	DET
ejpam-393	813	9	signature	signature	NOUN
ejpam-393	813	10	of	of	ADP
ejpam-393	813	11	boolean	boolean	ADJ
ejpam-393	813	12	algebras	algebra	NOUN
ejpam-393	813	13	expanded	expand	VERB
ejpam-393	813	14	by	by	ADP
ejpam-393	813	15	constant	constant	ADJ
ejpam-393	813	16	symbols	symbol	NOUN
ejpam-393	813	17	1u	1u	NUM
ejpam-393	813	18	for	for	ADP
ejpam-393	813	19	u	u	PROPN
ejpam-393	813	20	∈	∈	PROPN
ejpam-393	813	21	33	33	NUM
ejpam-393	813	22	and	and	CCONJ
ejpam-393	813	23	di	di	X
ejpam-393	813	24	j	j	PROPN
ejpam-393	813	25	for	for	ADP
ejpam-393	813	26	i	i	PROPN
ejpam-393	813	27	,	,	PUNCT
ejpam-393	813	28	j	j	PROPN
ejpam-393	813	29	∈	∈	PROPN
ejpam-393	813	30	3	3	NUM
ejpam-393	813	31	:	:	PUNCT
ejpam-393	813	32	(	(	PUNCT
ejpam-393	813	33	1	1	X
ejpam-393	813	34	)	)	PUNCT
ejpam-393	813	35	the	the	DET
ejpam-393	813	36	boolean	boolean	ADJ
ejpam-393	813	37	part	part	NOUN
ejpam-393	813	38	of	of	ADP
ejpam-393	813	39	¶	¶	PROPN
ejpam-393	813	40	is	be	AUX
ejpam-393	813	41	the	the	DET
ejpam-393	813	42	boolean	boolean	ADJ
ejpam-393	813	43	algebra	algebra	NOUN
ejpam-393	813	44	∏	∏	PROPN
ejpam-393	813	45	u∈33	u∈33	X
ejpam-393	813	46	au	au	PROPN
ejpam-393	813	47	,	,	PUNCT
ejpam-393	813	48	(	(	PUNCT
ejpam-393	813	49	2	2	X
ejpam-393	813	50	)	)	PUNCT
ejpam-393	814	1	1¶	1¶	NOUN
ejpam-393	814	2	u	u	NOUN
ejpam-393	814	3	=	=	PROPN
ejpam-393	814	4	f	f	PROPN
ejpam-393	814	5	(	(	PUNCT
ejpam-393	814	6	χm	χm	PROPN
ejpam-393	814	7	u	u	NOUN
ejpam-393	814	8	)	)	PUNCT
ejpam-393	814	9	=	=	PUNCT
ejpam-393	814	10	〈	〈	PROPN
ejpam-393	814	11	0	0	NUM
ejpam-393	814	12	,	,	PUNCT
ejpam-393	814	13	·	·	PUNCT
ejpam-393	814	14	·	·	PUNCT
ejpam-393	814	15	·	·	PUNCT
ejpam-393	814	16	0,1,0	0,1,0	NUM
ejpam-393	814	17	,	,	PUNCT
ejpam-393	814	18	·	·	PUNCT
ejpam-393	814	19	·	·	PUNCT
ejpam-393	814	20	·	·	PUNCT
ejpam-393	814	21	〉	〉	NOUN
ejpam-393	814	22	(	(	PUNCT
ejpam-393	814	23	with	with	ADP
ejpam-393	814	24	the	the	DET
ejpam-393	814	25	1	1	NUM
ejpam-393	814	26	in	in	ADP
ejpam-393	814	27	the	the	DET
ejpam-393	814	28	uth	uth	NOUN
ejpam-393	814	29	place	place	NOUN
ejpam-393	814	30	)	)	PUNCT
ejpam-393	814	31	for	for	ADP
ejpam-393	814	32	each	each	DET
ejpam-393	814	33	u	u	PROPN
ejpam-393	814	34	∈	∈	PROPN
ejpam-393	814	35	33	33	NUM
ejpam-393	814	36	,	,	PUNCT
ejpam-393	814	37	(	(	PUNCT
ejpam-393	814	38	3	3	X
ejpam-393	814	39	)	)	PUNCT
ejpam-393	814	40	d¶	d¶	NOUN
ejpam-393	815	1	i	i	PRON
ejpam-393	815	2	j	j	PROPN
ejpam-393	816	1	=	=	SYM
ejpam-393	816	2	f	f	PROPN
ejpam-393	816	3	(	(	PUNCT
ejpam-393	816	4	dai	dai	PROPN
ejpam-393	816	5	j	j	PROPN
ejpam-393	816	6	)	)	PUNCT
ejpam-393	816	7	for	for	ADP
ejpam-393	816	8	i	i	PRON
ejpam-393	816	9	,	,	PUNCT
ejpam-393	816	10	j	j	PROPN
ejpam-393	816	11	<	<	X
ejpam-393	816	12	3	3	X
ejpam-393	816	13	.	.	PUNCT
ejpam-393	817	1	we	we	PRON
ejpam-393	817	2	now	now	ADV
ejpam-393	817	3	show	show	VERB
ejpam-393	817	4	that	that	SCONJ
ejpam-393	817	5	a	a	PRON
ejpam-393	817	6	is	be	AUX
ejpam-393	817	7	interpretable	interpretable	ADJ
ejpam-393	817	8	in	in	ADP
ejpam-393	817	9	¶.	¶.	PROPN
ejpam-393	817	10	for	for	ADP
ejpam-393	817	11	this	this	PRON
ejpam-393	817	12	it	it	PRON
ejpam-393	817	13	is	be	AUX
ejpam-393	817	14	enough	enough	ADJ
ejpam-393	817	15	to	to	PART
ejpam-393	817	16	show	show	VERB
ejpam-393	817	17	that	that	SCONJ
ejpam-393	817	18	f	f	PROPN
ejpam-393	817	19	is	be	AUX
ejpam-393	817	20	one	one	NUM
ejpam-393	817	21	to	to	ADP
ejpam-393	817	22	one	one	NUM
ejpam-393	817	23	and	and	CCONJ
ejpam-393	817	24	that	that	DET
ejpam-393	817	25	rng	rng	PROPN
ejpam-393	817	26	(	(	PUNCT
ejpam-393	817	27	f	f	PROPN
ejpam-393	817	28	)	)	PUNCT
ejpam-393	817	29	(	(	PUNCT
ejpam-393	817	30	range	range	NOUN
ejpam-393	817	31	of	of	ADP
ejpam-393	817	32	f	f	PROPN
ejpam-393	817	33	)	)	PUNCT
ejpam-393	817	34	and	and	CCONJ
ejpam-393	817	35	the	the	DET
ejpam-393	817	36	f	f	PROPN
ejpam-393	817	37	-images	-image	NOUN
ejpam-393	817	38	of	of	ADP
ejpam-393	817	39	the	the	DET
ejpam-393	817	40	graphs	graph	NOUN
ejpam-393	817	41	of	of	ADP
ejpam-393	817	42	the	the	DET
ejpam-393	817	43	cylindric	cylindric	ADJ
ejpam-393	817	44	algebra	algebra	NOUN
ejpam-393	817	45	functions	function	NOUN
ejpam-393	817	46	in	in	ADP
ejpam-393	817	47	a	a	PRON
ejpam-393	817	48	are	be	AUX
ejpam-393	817	49	definable	definable	ADJ
ejpam-393	817	50	in	in	ADP
ejpam-393	817	51	¶.	¶.	PROPN
ejpam-393	817	52	since	since	SCONJ
ejpam-393	817	53	the	the	DET
ejpam-393	817	54	χm	χm	PROPN
ejpam-393	817	55	u	u	PROPN
ejpam-393	817	56	partition	partition	NOUN
ejpam-393	817	57	the	the	DET
ejpam-393	817	58	unit	unit	NOUN
ejpam-393	817	59	of	of	ADP
ejpam-393	817	60	a	a	PRON
ejpam-393	817	61	,	,	PUNCT
ejpam-393	817	62	each	each	PRON
ejpam-393	817	63	a	a	DET
ejpam-393	817	64	∈	∈	PROPN
ejpam-393	817	65	a	a	PRON
ejpam-393	817	66	has	have	VERB
ejpam-393	817	67	a	a	DET
ejpam-393	817	68	unique	unique	ADJ
ejpam-393	817	69	expression	expression	NOUN
ejpam-393	817	70	in	in	ADP
ejpam-393	817	71	the	the	DET
ejpam-393	817	72	form	form	NOUN
ejpam-393	817	73	∑	∑	PUNCT
ejpam-393	817	74	u∈33(a.χm	u∈33(a.χm	PROPN
ejpam-393	817	75	u	u	NOUN
ejpam-393	817	76	)	)	PUNCT
ejpam-393	817	77	,	,	PUNCT
ejpam-393	817	78	and	and	CCONJ
ejpam-393	817	79	it	it	PRON
ejpam-393	817	80	follows	follow	VERB
ejpam-393	817	81	that	that	SCONJ
ejpam-393	817	82	f	f	PROPN
ejpam-393	817	83	is	be	AUX
ejpam-393	817	84	boolean	boolean	ADJ
ejpam-393	817	85	isomorphism	isomorphism	NOUN
ejpam-393	817	86	:	:	PUNCT
ejpam-393	817	87	bool(a)→	bool(a)→	PROPN
ejpam-393	817	88	∏	∏	PROPN
ejpam-393	817	89	u∈33	u∈33	X
ejpam-393	817	90	au	au	PROPN
ejpam-393	817	91	.	.	PUNCT
ejpam-393	818	1	so	so	ADV
ejpam-393	818	2	the	the	DET
ejpam-393	818	3	f	f	PROPN
ejpam-393	818	4	-images	-image	NOUN
ejpam-393	818	5	of	of	ADP
ejpam-393	818	6	the	the	DET
ejpam-393	818	7	graphs	graph	NOUN
ejpam-393	818	8	of	of	ADP
ejpam-393	818	9	the	the	DET
ejpam-393	818	10	boolean	boolean	ADJ
ejpam-393	818	11	functions	function	NOUN
ejpam-393	818	12	on	on	ADP
ejpam-393	818	13	a	a	PRON
ejpam-393	818	14	are	be	AUX
ejpam-393	818	15	trivially	trivially	ADV
ejpam-393	818	16	t.	t.	PROPN
ejpam-393	818	17	ahmed	ahmed	PROPN
ejpam-393	818	18	/	/	SYM
ejpam-393	818	19	eur	eur	PROPN
ejpam-393	818	20	.	.	PUNCT
ejpam-393	819	1	j.	j.	PROPN
ejpam-393	819	2	pure	pure	PROPN
ejpam-393	819	3	appl	appl	PROPN
ejpam-393	819	4	.	.	PROPN
ejpam-393	819	5	math	math	PROPN
ejpam-393	819	6	,	,	PUNCT
ejpam-393	819	7	3	3	NUM
ejpam-393	819	8	(	(	PUNCT
ejpam-393	819	9	2010	2010	NUM
ejpam-393	819	10	)	)	PUNCT
ejpam-393	819	11	,	,	PUNCT
ejpam-393	819	12	853	853	NUM
ejpam-393	819	13	-	-	SYM
ejpam-393	819	14	880	880	NUM
ejpam-393	819	15	875	875	NUM
ejpam-393	819	16	definable	definable	ADJ
ejpam-393	819	17	.	.	PUNCT
ejpam-393	820	1	f	f	PROPN
ejpam-393	820	2	is	be	AUX
ejpam-393	820	3	bijective	bijective	ADJ
ejpam-393	820	4	so	so	ADV
ejpam-393	820	5	rng	rng	PROPN
ejpam-393	820	6	(	(	PUNCT
ejpam-393	820	7	f	f	PROPN
ejpam-393	820	8	)	)	PUNCT
ejpam-393	820	9	is	be	AUX
ejpam-393	820	10	definable	definable	ADJ
ejpam-393	820	11	,	,	PUNCT
ejpam-393	820	12	by	by	ADP
ejpam-393	820	13	x	x	X
ejpam-393	821	1	=	=	PUNCT
ejpam-393	821	2	x	x	PROPN
ejpam-393	821	3	.	.	PUNCT
ejpam-393	822	1	for	for	ADP
ejpam-393	822	2	the	the	DET
ejpam-393	822	3	diagonals	diagonal	NOUN
ejpam-393	822	4	,	,	PUNCT
ejpam-393	822	5	f	f	PROPN
ejpam-393	822	6	(	(	PUNCT
ejpam-393	822	7	dai	dai	PROPN
ejpam-393	822	8	j	j	PROPN
ejpam-393	822	9	)	)	PUNCT
ejpam-393	822	10	is	be	AUX
ejpam-393	822	11	definable	definable	ADJ
ejpam-393	822	12	by	by	ADP
ejpam-393	822	13	x	x	SYM
ejpam-393	822	14	=	=	SYM
ejpam-393	822	15	di	di	PROPN
ejpam-393	822	16	j.	j.	PROPN
ejpam-393	822	17	finally	finally	ADV
ejpam-393	822	18	we	we	PRON
ejpam-393	822	19	consider	consider	VERB
ejpam-393	822	20	cylindrifications	cylindrification	NOUN
ejpam-393	822	21	.	.	PUNCT
ejpam-393	823	1	for	for	ADP
ejpam-393	823	2	s	s	NOUN
ejpam-393	823	3	⊆	⊆	NUM
ejpam-393	823	4	33	33	NUM
ejpam-393	823	5	,	,	PUNCT
ejpam-393	823	6	i	i	PRON
ejpam-393	823	7	<	<	X
ejpam-393	823	8	3	3	NUM
ejpam-393	823	9	,	,	PUNCT
ejpam-393	823	10	let	let	VERB
ejpam-393	823	11	ts	ts	PART
ejpam-393	823	12	be	be	AUX
ejpam-393	823	13	the	the	DET
ejpam-393	823	14	closed	closed	ADJ
ejpam-393	823	15	term	term	NOUN
ejpam-393	823	16	∑	∑	PUNCT
ejpam-393	823	17	{	{	PUNCT
ejpam-393	823	18	1v	1v	NUM
ejpam-393	823	19	:	:	PUNCT
ejpam-393	823	20	v	v	NUM
ejpam-393	823	21	∈	∈	PROPN
ejpam-393	823	22	33	33	NUM
ejpam-393	823	23	,	,	PUNCT
ejpam-393	823	24	v	v	PRON
ejpam-393	823	25	≡i	≡i	PROPN
ejpam-393	823	26	u	u	NOUN
ejpam-393	823	27	for	for	ADP
ejpam-393	823	28	some	some	DET
ejpam-393	823	29	u	u	NOUN
ejpam-393	823	30	∈	∈	NOUN
ejpam-393	823	31	s	s	PART
ejpam-393	823	32	}	}	PUNCT
ejpam-393	823	33	.	.	PUNCT
ejpam-393	824	1	let	let	VERB
ejpam-393	824	2	ηi(x	ηi(x	NOUN
ejpam-393	824	3	,	,	PUNCT
ejpam-393	824	4	y	y	NOUN
ejpam-393	824	5	)	)	PUNCT
ejpam-393	825	1	=	=	PUNCT
ejpam-393	826	1	∧	∧	NOUN
ejpam-393	826	2	s⊆33	s⊆33	VERB
ejpam-393	826	3	(	(	PUNCT
ejpam-393	826	4	∧	∧	PROPN
ejpam-393	826	5	u∈s	u∈s	ADJ
ejpam-393	826	6	x	x	X
ejpam-393	826	7	.1u	.1u	NOUN
ejpam-393	826	8	6=	6=	NUM
ejpam-393	826	9	0∧	0∧	NOUN
ejpam-393	826	10	∧	∧	PROPN
ejpam-393	826	11	u∈33rs	u∈33rs	NOUN
ejpam-393	826	12	x	x	X
ejpam-393	826	13	.1u	.1u	NOUN
ejpam-393	826	14	=	=	SYM
ejpam-393	826	15	0−→	0−→	PROPN
ejpam-393	826	16	y	y	PROPN
ejpam-393	826	17	=	=	PUNCT
ejpam-393	826	18	ts	ts	PROPN
ejpam-393	826	19	)	)	PUNCT
ejpam-393	826	20	.	.	PUNCT
ejpam-393	827	1	we	we	PRON
ejpam-393	827	2	claim	claim	VERB
ejpam-393	827	3	that	that	SCONJ
ejpam-393	827	4	for	for	ADP
ejpam-393	827	5	all	all	DET
ejpam-393	827	6	a	a	DET
ejpam-393	827	7	∈	∈	PROPN
ejpam-393	827	8	a	a	PRON
ejpam-393	827	9	,	,	PUNCT
ejpam-393	827	10	b	b	PROPN
ejpam-393	827	11	∈	∈	PROPN
ejpam-393	827	12	p	p	NOUN
ejpam-393	827	13	,	,	PUNCT
ejpam-393	827	14	we	we	PRON
ejpam-393	827	15	have	have	VERB
ejpam-393	827	16	¶	¶	NUM
ejpam-393	827	17	|=	|=	NOUN
ejpam-393	827	18	ηi	ηi	PROPN
ejpam-393	827	19	(	(	PUNCT
ejpam-393	827	20	f	f	PROPN
ejpam-393	827	21	(	(	PUNCT
ejpam-393	827	22	a	a	NOUN
ejpam-393	827	23	)	)	PUNCT
ejpam-393	827	24	,	,	PUNCT
ejpam-393	827	25	b	b	X
ejpam-393	827	26	)	)	PUNCT
ejpam-393	827	27	iff	iff	PROPN
ejpam-393	827	28	b	b	PROPN
ejpam-393	827	29	=	=	SYM
ejpam-393	827	30	f	f	PROPN
ejpam-393	827	31	(	(	PUNCT
ejpam-393	827	32	cai	cai	X
ejpam-393	827	33	a	a	NOUN
ejpam-393	827	34	)	)	PUNCT
ejpam-393	827	35	.	.	PUNCT
ejpam-393	828	1	to	to	PART
ejpam-393	828	2	see	see	VERB
ejpam-393	828	3	this	this	PRON
ejpam-393	828	4	,	,	PUNCT
ejpam-393	828	5	let	let	VERB
ejpam-393	828	6	f	f	PROPN
ejpam-393	828	7	(	(	PUNCT
ejpam-393	828	8	a	a	NOUN
ejpam-393	828	9	)	)	PUNCT
ejpam-393	828	10	=	=	PUNCT
ejpam-393	828	11	〈	〈	PROPN
ejpam-393	828	12	au〉u∈33	au〉u∈33	PROPN
ejpam-393	828	13	,	,	PUNCT
ejpam-393	828	14	say	say	VERB
ejpam-393	828	15	.	.	PUNCT
ejpam-393	829	1	so	so	ADV
ejpam-393	829	2	in	in	ADP
ejpam-393	829	3	a	a	PRON
ejpam-393	829	4	we	we	PRON
ejpam-393	829	5	have	have	VERB
ejpam-393	829	6	a	a	DET
ejpam-393	829	7	=	=	SYM
ejpam-393	829	8	∑	∑	PUNCT
ejpam-393	829	9	u	u	NOUN
ejpam-393	829	10	au	au	PROPN
ejpam-393	829	11	.	.	PROPN
ejpam-393	830	1	let	let	VERB
ejpam-393	830	2	u	u	PRON
ejpam-393	830	3	be	be	AUX
ejpam-393	830	4	given	give	VERB
ejpam-393	830	5	;	;	PUNCT
ejpam-393	830	6	au	au	X
ejpam-393	830	7	has	have	VERB
ejpam-393	830	8	the	the	DET
ejpam-393	830	9	form	form	NOUN
ejpam-393	830	10	(	(	PUNCT
ejpam-393	830	11	χi	χi	NOUN
ejpam-393	830	12	∧φ	∧φ	NOUN
ejpam-393	830	13	)	)	PUNCT
ejpam-393	830	14	m	m	VERB
ejpam-393	830	15	for	for	ADP
ejpam-393	830	16	some	some	DET
ejpam-393	830	17	φ	φ	PROPN
ejpam-393	830	18	∈	∈	PROPN
ejpam-393	830	19	l3	l3	NOUN
ejpam-393	830	20	,	,	PUNCT
ejpam-393	830	21	so	so	SCONJ
ejpam-393	830	22	ca	can	AUX
ejpam-393	830	23	i	i	PRON
ejpam-393	830	24	(	(	PUNCT
ejpam-393	830	25	au	au	PROPN
ejpam-393	830	26	)	)	PUNCT
ejpam-393	830	27	=	=	SYM
ejpam-393	830	28	(	(	PUNCT
ejpam-393	830	29	∃x	∃x	X
ejpam-393	830	30	i(χu	i(χu	NOUN
ejpam-393	830	31	∧φ	∧φ	NOUN
ejpam-393	830	32	)	)	PUNCT
ejpam-393	830	33	)	)	PUNCT
ejpam-393	830	34	m.	m.	NOUN
ejpam-393	830	35	by	by	ADP
ejpam-393	830	36	property	property	NOUN
ejpam-393	830	37	6	6	NUM
ejpam-393	830	38	of	of	ADP
ejpam-393	830	39	lemma	lemma	PROPN
ejpam-393	830	40	9	9	NUM
ejpam-393	830	41	,	,	PUNCT
ejpam-393	830	42	if	if	SCONJ
ejpam-393	830	43	au	au	ADP
ejpam-393	830	44	6=	6=	NUM
ejpam-393	830	45	0	0	NUM
ejpam-393	830	46	,	,	PUNCT
ejpam-393	830	47	this	this	PRON
ejpam-393	830	48	is	be	AUX
ejpam-393	830	49	(	(	PUNCT
ejpam-393	830	50	∃x	∃x	PROPN
ejpam-393	830	51	iχu	iχu	NOUN
ejpam-393	830	52	)	)	PUNCT
ejpam-393	830	53	m	m	VERB
ejpam-393	830	54	;	;	PUNCT
ejpam-393	830	55	by	by	ADP
ejpam-393	830	56	property	property	NOUN
ejpam-393	830	57	5	5	NUM
ejpam-393	830	58	,	,	PUNCT
ejpam-393	830	59	this	this	PRON
ejpam-393	830	60	is	be	AUX
ejpam-393	830	61	(	(	PUNCT
ejpam-393	830	62	∨	∨	PROPN
ejpam-393	830	63	v∈33,v≡iu	v∈33,v≡iu	PROPN
ejpam-393	830	64	χv	χv	NOUN
ejpam-393	830	65	)	)	PUNCT
ejpam-393	830	66	m.	m.	NOUN
ejpam-393	830	67	let	let	VERB
ejpam-393	830	68	s	s	PRON
ejpam-393	830	69	=	=	PUNCT
ejpam-393	830	70	{	{	PUNCT
ejpam-393	830	71	u	u	NOUN
ejpam-393	830	72	∈	∈	PROPN
ejpam-393	830	73	33	33	NUM
ejpam-393	830	74	:	:	PUNCT
ejpam-393	830	75	au	au	PROPN
ejpam-393	830	76	6=	6=	ADP
ejpam-393	830	77	0	0	NUM
ejpam-393	830	78	}	}	PUNCT
ejpam-393	830	79	.	.	PUNCT
ejpam-393	831	1	by	by	ADP
ejpam-393	831	2	normality	normality	NOUN
ejpam-393	831	3	and	and	CCONJ
ejpam-393	831	4	additivity	additivity	NOUN
ejpam-393	831	5	of	of	ADP
ejpam-393	831	6	cylindrifications	cylindrification	NOUN
ejpam-393	831	7	we	we	PRON
ejpam-393	831	8	have	have	VERB
ejpam-393	831	9	,	,	PUNCT
ejpam-393	831	10	ca	can	AUX
ejpam-393	831	11	i	i	PRON
ejpam-393	831	12	(	(	PUNCT
ejpam-393	831	13	a	a	X
ejpam-393	831	14	)	)	PUNCT
ejpam-393	831	15	=	=	PUNCT
ejpam-393	831	16	∑	∑	PUNCT
ejpam-393	831	17	u∈33	u∈33	INTJ
ejpam-393	831	18	ca	can	AUX
ejpam-393	831	19	i	i	PRON
ejpam-393	831	20	au	au	VERB
ejpam-393	831	21	=	=	PUNCT
ejpam-393	831	22	∑	∑	PRON
ejpam-393	831	23	u∈s	u∈s	ADJ
ejpam-393	831	24	ca	can	AUX
ejpam-393	831	25	i	i	PRON
ejpam-393	831	26	au	au	VERB
ejpam-393	831	27	=	=	PUNCT
ejpam-393	831	28	∑	∑	NOUN
ejpam-393	831	29	u∈s	u∈s	ADJ
ejpam-393	831	30	(	(	PUNCT
ejpam-393	831	31	∑	∑	ADV
ejpam-393	831	32	v∈33,v≡iu	v∈33,v≡iu	VERB
ejpam-393	831	33	χm	χm	NOUN
ejpam-393	831	34	v	v	NOUN
ejpam-393	831	35	)	)	PUNCT
ejpam-393	831	36	=	=	PUNCT
ejpam-393	831	37	∑	∑	PUNCT
ejpam-393	831	38	{	{	PUNCT
ejpam-393	831	39	χm	χm	NOUN
ejpam-393	831	40	v	v	NOUN
ejpam-393	831	41	:	:	PUNCT
ejpam-393	831	42	v	v	NUM
ejpam-393	831	43	∈	∈	PROPN
ejpam-393	831	44	33	33	NUM
ejpam-393	831	45	,	,	PUNCT
ejpam-393	831	46	v	v	PRON
ejpam-393	831	47	≡i	≡i	PROPN
ejpam-393	831	48	u	u	NOUN
ejpam-393	831	49	for	for	ADP
ejpam-393	831	50	some	some	DET
ejpam-393	831	51	u	u	NOUN
ejpam-393	831	52	∈	∈	NOUN
ejpam-393	831	53	s	s	PART
ejpam-393	831	54	}	}	PUNCT
ejpam-393	831	55	.	.	PUNCT
ejpam-393	832	1	so	so	ADV
ejpam-393	832	2	¶	¶	PROPN
ejpam-393	832	3	|=	|=	PUNCT
ejpam-393	832	4	f	f	X
ejpam-393	832	5	(	(	PUNCT
ejpam-393	832	6	ca	can	AUX
ejpam-393	832	7	i	i	PRON
ejpam-393	832	8	a	a	X
ejpam-393	832	9	)	)	PUNCT
ejpam-393	832	10	=	=	SYM
ejpam-393	832	11	ts	t	NOUN
ejpam-393	832	12	.	.	PUNCT
ejpam-393	833	1	hence	hence	ADV
ejpam-393	833	2	¶	¶	PROPN
ejpam-393	833	3	|=	|=	X
ejpam-393	833	4	ηi	ηi	PROPN
ejpam-393	833	5	(	(	PUNCT
ejpam-393	833	6	f	f	PROPN
ejpam-393	833	7	(	(	PUNCT
ejpam-393	833	8	a	a	PROPN
ejpam-393	833	9	)	)	PUNCT
ejpam-393	833	10	,	,	PUNCT
ejpam-393	833	11	f	f	PROPN
ejpam-393	833	12	(	(	PUNCT
ejpam-393	833	13	ca	can	AUX
ejpam-393	833	14	i	i	PRON
ejpam-393	833	15	a	a	X
ejpam-393	833	16	)	)	PUNCT
ejpam-393	833	17	)	)	PUNCT
ejpam-393	833	18	.	.	PUNCT
ejpam-393	834	1	conversely	conversely	ADV
ejpam-393	834	2	,	,	PUNCT
ejpam-393	834	3	if	if	SCONJ
ejpam-393	834	4	¶	¶	PROPN
ejpam-393	834	5	|=	|=	X
ejpam-393	834	6	ηi	ηi	X
ejpam-393	834	7	(	(	PUNCT
ejpam-393	834	8	f	f	PROPN
ejpam-393	834	9	(	(	PUNCT
ejpam-393	834	10	a	a	NOUN
ejpam-393	834	11	)	)	PUNCT
ejpam-393	834	12	,	,	PUNCT
ejpam-393	834	13	b	b	X
ejpam-393	834	14	)	)	PUNCT
ejpam-393	834	15	,	,	PUNCT
ejpam-393	834	16	we	we	PRON
ejpam-393	834	17	require	require	VERB
ejpam-393	834	18	b	b	NOUN
ejpam-393	834	19	=	=	SYM
ejpam-393	834	20	f	f	PROPN
ejpam-393	834	21	(	(	PUNCT
ejpam-393	834	22	cia	cia	PROPN
ejpam-393	834	23	)	)	PUNCT
ejpam-393	834	24	.	.	PUNCT
ejpam-393	835	1	now	now	ADV
ejpam-393	835	2	s	s	VERB
ejpam-393	835	3	is	be	AUX
ejpam-393	835	4	the	the	DET
ejpam-393	835	5	unique	unique	ADJ
ejpam-393	835	6	subset	subset	NOUN
ejpam-393	835	7	of	of	ADP
ejpam-393	835	8	33	33	NUM
ejpam-393	835	9	such	such	ADJ
ejpam-393	835	10	that	that	SCONJ
ejpam-393	835	11	¶	¶	PROPN
ejpam-393	835	12	|=	|=	PUNCT
ejpam-393	835	13	∧	∧	PROPN
ejpam-393	835	14	u∈s	u∈s	ADJ
ejpam-393	835	15	f	f	PROPN
ejpam-393	835	16	(	(	PUNCT
ejpam-393	835	17	a).1u	a).1u	PROPN
ejpam-393	835	18	6=	6=	NUM
ejpam-393	835	19	0∧	0∧	NOUN
ejpam-393	835	20	∧	∧	PROPN
ejpam-393	835	21	u∈33rs	u∈33rs	NOUN
ejpam-393	835	22	f	f	PROPN
ejpam-393	835	23	(	(	PUNCT
ejpam-393	835	24	a).1u	a).1u	NOUN
ejpam-393	835	25	=	=	NOUN
ejpam-393	835	26	0	0	X
ejpam-393	835	27	.	.	PUNCT
ejpam-393	836	1	so	so	ADV
ejpam-393	836	2	we	we	PRON
ejpam-393	836	3	obtain	obtain	VERB
ejpam-393	836	4	b	b	NOUN
ejpam-393	836	5	=	=	NOUN
ejpam-393	836	6	ts	ts	X
ejpam-393	836	7	=	=	SYM
ejpam-393	836	8	f	f	PROPN
ejpam-393	836	9	(	(	PUNCT
ejpam-393	836	10	ca	can	AUX
ejpam-393	836	11	i	i	PRON
ejpam-393	836	12	a	a	X
ejpam-393	836	13	)	)	PUNCT
ejpam-393	836	14	.	.	PUNCT
ejpam-393	837	1	we	we	PRON
ejpam-393	837	2	have	have	AUX
ejpam-393	837	3	proved	prove	VERB
ejpam-393	837	4	that	that	SCONJ
ejpam-393	837	5	¶	¶	PROPN
ejpam-393	837	6	is	be	AUX
ejpam-393	837	7	interpretable	interpretable	ADJ
ejpam-393	837	8	in	in	ADP
ejpam-393	837	9	a.	a.	NOUN
ejpam-393	837	10	furthermore	furthermore	ADV
ejpam-393	837	11	it	it	PRON
ejpam-393	837	12	is	be	AUX
ejpam-393	837	13	easy	easy	ADJ
ejpam-393	837	14	to	to	PART
ejpam-393	837	15	see	see	VERB
ejpam-393	837	16	that	that	SCONJ
ejpam-393	837	17	the	the	DET
ejpam-393	837	18	interpretation	interpretation	NOUN
ejpam-393	837	19	is	be	AUX
ejpam-393	837	20	one	one	NUM
ejpam-393	837	21	dimensional	dimensional	ADJ
ejpam-393	837	22	and	and	CCONJ
ejpam-393	837	23	quantifier	quantifier	VERB
ejpam-393	837	24	free	free	ADJ
ejpam-393	837	25	.	.	PUNCT
ejpam-393	838	1	next	next	ADV
ejpam-393	838	2	we	we	PRON
ejpam-393	838	3	extract	extract	VERB
ejpam-393	838	4	an	an	DET
ejpam-393	838	5	algebra	algebra	PROPN
ejpam-393	838	6	b	b	PROPN
ejpam-393	838	7	elementary	elementary	ADJ
ejpam-393	838	8	equivalent	equivalent	NOUN
ejpam-393	838	9	to	to	ADP
ejpam-393	838	10	a	a	PRON
ejpam-393	838	11	that	that	PRON
ejpam-393	838	12	is	be	AUX
ejpam-393	838	13	not	not	PART
ejpam-393	838	14	a	a	DET
ejpam-393	838	15	neat	neat	ADJ
ejpam-393	838	16	reduct	reduct	NOUN
ejpam-393	838	17	i.e.	i.e.	X
ejpam-393	838	18	not	not	PART
ejpam-393	838	19	in	in	ADP
ejpam-393	838	20	nr3ca4	nr3ca4	NOUN
ejpam-393	838	21	.	.	PUNCT
ejpam-393	839	1	also	also	ADV
ejpam-393	839	2	rdrscb	rdrscb	VERB
ejpam-393	839	3	/∈	/∈	PUNCT
ejpam-393	840	1	nr3rsc5	nr3rsc5	PROPN
ejpam-393	840	2	.	.	PUNCT
ejpam-393	841	1	let	let	VERB
ejpam-393	841	2	i	i	PRON
ejpam-393	841	3	d	d	PROPN
ejpam-393	841	4	∈	∈	PROPN
ejpam-393	841	5	33	33	NUM
ejpam-393	841	6	be	be	AUX
ejpam-393	841	7	the	the	DET
ejpam-393	841	8	identity	identity	NOUN
ejpam-393	841	9	map	map	NOUN
ejpam-393	841	10	on	on	ADP
ejpam-393	841	11	3	3	NUM
ejpam-393	841	12	.	.	PUNCT
ejpam-393	842	1	choose	choose	VERB
ejpam-393	842	2	any	any	DET
ejpam-393	842	3	countable	countable	ADJ
ejpam-393	842	4	boolean	boolean	ADJ
ejpam-393	842	5	elementary	elementary	ADJ
ejpam-393	842	6	subalgebra	subalgebra	NOUN
ejpam-393	842	7	of	of	ADP
ejpam-393	842	8	ai	ai	PROPN
ejpam-393	842	9	d	d	PROPN
ejpam-393	842	10	,	,	PUNCT
ejpam-393	842	11	bi	bi	NOUN
ejpam-393	842	12	d	d	PROPN
ejpam-393	842	13	say	say	VERB
ejpam-393	842	14	.	.	PUNCT
ejpam-393	843	1	thus	thus	ADV
ejpam-393	843	2	bi	bi	PROPN
ejpam-393	843	3	d	d	PROPN
ejpam-393	843	4	�	�	PROPN
ejpam-393	843	5	ai	ai	VERB
ejpam-393	843	6	d	d	PROPN
ejpam-393	843	7	.	.	PUNCT
ejpam-393	844	1	by	by	ADP
ejpam-393	844	2	lemma	lemma	PROPN
ejpam-393	844	3	9	9	NUM
ejpam-393	844	4	q	q	NOUN
ejpam-393	844	5	=	=	PUNCT
ejpam-393	844	6	(	(	PUNCT
ejpam-393	844	7	(	(	PUNCT
ejpam-393	844	8	bi	bi	NOUN
ejpam-393	844	9	d	d	PROPN
ejpam-393	844	10	×	×	PROPN
ejpam-393	844	11	∏	∏	PROPN
ejpam-393	844	12	u∈33ri	u∈33ri	NOUN
ejpam-393	844	13	d	d	PROPN
ejpam-393	844	14	au	au	PROPN
ejpam-393	844	15	)	)	PUNCT
ejpam-393	844	16	,	,	PUNCT
ejpam-393	844	17	1u	1u	NUM
ejpam-393	844	18	,	,	PUNCT
ejpam-393	844	19	di	di	X
ejpam-393	844	20	j)u∈33,i	j)u∈33,i	PROPN
ejpam-393	844	21	,	,	PUNCT
ejpam-393	844	22	j<3	j<3	PROPN
ejpam-393	844	23	≡	≡	PROPN
ejpam-393	844	24	(	(	PUNCT
ejpam-393	844	25	∏	∏	PROPN
ejpam-393	844	26	u∈33	u∈33	X
ejpam-393	844	27	au	au	PROPN
ejpam-393	844	28	)	)	PUNCT
ejpam-393	844	29	)	)	PUNCT
ejpam-393	844	30	,	,	PUNCT
ejpam-393	844	31	1u	1u	NUM
ejpam-393	844	32	,	,	PUNCT
ejpam-393	844	33	di	di	X
ejpam-393	844	34	j)u∈33,i	j)u∈33,i	PROPN
ejpam-393	844	35	,	,	PUNCT
ejpam-393	844	36	j<3	j<3	PROPN
ejpam-393	845	1	=	=	SYM
ejpam-393	845	2	p.	p.	NOUN
ejpam-393	845	3	(	(	PUNCT
ejpam-393	845	4	note	note	VERB
ejpam-393	845	5	that	that	SCONJ
ejpam-393	845	6	the	the	DET
ejpam-393	845	7	i	i	PROPN
ejpam-393	845	8	d	d	NOUN
ejpam-393	845	9	th	th	X
ejpam-393	845	10	coordinate	coordinate	NOUN
ejpam-393	845	11	of	of	ADP
ejpam-393	845	12	each	each	DET
ejpam-393	845	13	constant	constant	ADJ
ejpam-393	845	14	is	be	AUX
ejpam-393	845	15	0	0	NUM
ejpam-393	845	16	or	or	CCONJ
ejpam-393	845	17	1	1	NUM
ejpam-393	845	18	,	,	PUNCT
ejpam-393	845	19	so	so	ADV
ejpam-393	845	20	the	the	DET
ejpam-393	845	21	constants	constant	NOUN
ejpam-393	845	22	do	do	AUX
ejpam-393	845	23	lie	lie	VERB
ejpam-393	845	24	in	in	ADP
ejpam-393	845	25	q.	q.	PROPN
ejpam-393	845	26	)	)	PUNCT
ejpam-393	845	27	let	let	VERB
ejpam-393	845	28	b	b	X
ejpam-393	845	29	be	be	AUX
ejpam-393	845	30	the	the	DET
ejpam-393	845	31	result	result	NOUN
ejpam-393	845	32	of	of	ADP
ejpam-393	845	33	applying	apply	VERB
ejpam-393	845	34	the	the	DET
ejpam-393	845	35	interpretation	interpretation	NOUN
ejpam-393	845	36	given	give	VERB
ejpam-393	845	37	above	above	ADV
ejpam-393	845	38	to	to	ADP
ejpam-393	845	39	q.	q.	PROPN
ejpam-393	845	40	then	then	ADV
ejpam-393	845	41	b	b	PROPN
ejpam-393	845	42	≡	≡	PROPN
ejpam-393	845	43	a	a	DET
ejpam-393	845	44	as	as	ADP
ejpam-393	845	45	cylindric	cylindric	ADJ
ejpam-393	845	46	algebras	algebra	NOUN
ejpam-393	845	47	.	.	PUNCT
ejpam-393	846	1	now	now	ADV
ejpam-393	846	2	we	we	PRON
ejpam-393	846	3	show	show	VERB
ejpam-393	846	4	that	that	SCONJ
ejpam-393	846	5	b	b	NOUN
ejpam-393	846	6	can	can	AUX
ejpam-393	846	7	not	not	PART
ejpam-393	846	8	be	be	AUX
ejpam-393	846	9	a	a	DET
ejpam-393	846	10	neat	neat	ADJ
ejpam-393	846	11	reduct	reduct	NOUN
ejpam-393	846	12	,	,	PUNCT
ejpam-393	846	13	in	in	ADP
ejpam-393	846	14	fact	fact	NOUN
ejpam-393	846	15	we	we	PRON
ejpam-393	846	16	show	show	VERB
ejpam-393	846	17	that	that	PRON
ejpam-393	846	18	b	b	X
ejpam-393	846	19	/∈	/∈	PUNCT
ejpam-393	846	20	nr3caβ	nr3caβ	PROPN
ejpam-393	846	21	t.	t.	PROPN
ejpam-393	846	22	ahmed	ahmed	PROPN
ejpam-393	846	23	/	/	SYM
ejpam-393	846	24	eur	eur	PROPN
ejpam-393	846	25	.	.	PUNCT
ejpam-393	847	1	j.	j.	PROPN
ejpam-393	847	2	pure	pure	PROPN
ejpam-393	847	3	appl	appl	PROPN
ejpam-393	847	4	.	.	PROPN
ejpam-393	847	5	math	math	PROPN
ejpam-393	847	6	,	,	PUNCT
ejpam-393	847	7	3	3	NUM
ejpam-393	847	8	(	(	PUNCT
ejpam-393	847	9	2010	2010	NUM
ejpam-393	847	10	)	)	PUNCT
ejpam-393	847	11	,	,	PUNCT
ejpam-393	847	12	853	853	NUM
ejpam-393	847	13	-	-	SYM
ejpam-393	847	14	880	880	NUM
ejpam-393	847	15	876	876	NUM
ejpam-393	847	16	for	for	ADP
ejpam-393	847	17	any	any	DET
ejpam-393	847	18	β	β	X
ejpam-393	847	19	>	>	X
ejpam-393	847	20	3	3	NUM
ejpam-393	847	21	,	,	PUNCT
ejpam-393	847	22	while	while	SCONJ
ejpam-393	847	23	rdrscb	rdrscb	NOUN
ejpam-393	847	24	/∈	/∈	PUNCT
ejpam-393	848	1	nr3rscβ	nr3rscβ	X
ejpam-393	848	2	for	for	ADP
ejpam-393	848	3	β	β	X
ejpam-393	848	4	>	>	X
ejpam-393	848	5	4	4	NUM
ejpam-393	848	6	.	.	PUNCT
ejpam-393	848	7	we	we	PRON
ejpam-393	848	8	settle	settle	VERB
ejpam-393	848	9	first	first	ADV
ejpam-393	848	10	the	the	DET
ejpam-393	848	11	cylindric	cylindric	ADJ
ejpam-393	848	12	case	case	NOUN
ejpam-393	848	13	.	.	PUNCT
ejpam-393	849	1	assume	assume	VERB
ejpam-393	849	2	for	for	ADP
ejpam-393	849	3	contradiction	contradiction	NOUN
ejpam-393	849	4	that	that	PRON
ejpam-393	849	5	b	b	X
ejpam-393	849	6	=	=	PUNCT
ejpam-393	849	7	nr3d	nr3d	PROPN
ejpam-393	849	8	for	for	ADP
ejpam-393	849	9	some	some	DET
ejpam-393	849	10	d	d	PROPN
ejpam-393	849	11	∈	∈	PROPN
ejpam-393	849	12	caβ	caβ	NOUN
ejpam-393	849	13	;	;	PUNCT
ejpam-393	849	14	with	with	ADP
ejpam-393	849	15	β	β	X
ejpam-393	849	16	>	>	X
ejpam-393	849	17	3	3	X
ejpam-393	849	18	.	.	X
ejpam-393	849	19	note	note	VERB
ejpam-393	849	20	that	that	SCONJ
ejpam-393	849	21	d	d	NOUN
ejpam-393	849	22	may	may	AUX
ejpam-393	849	23	not	not	PART
ejpam-393	849	24	be	be	AUX
ejpam-393	849	25	representable	representable	ADJ
ejpam-393	849	26	.	.	PUNCT
ejpam-393	850	1	it	it	PRON
ejpam-393	850	2	is	be	AUX
ejpam-393	850	3	only	only	ADV
ejpam-393	850	4	here	here	ADV
ejpam-393	850	5	that	that	SCONJ
ejpam-393	850	6	we	we	PRON
ejpam-393	850	7	deal	deal	VERB
ejpam-393	850	8	with	with	ADP
ejpam-393	850	9	possibly	possibly	ADV
ejpam-393	850	10	non	non	ADJ
ejpam-393	850	11	-	-	ADJ
ejpam-393	850	12	representable	representable	ADJ
ejpam-393	850	13	algebras	algebra	NOUN
ejpam-393	850	14	.	.	PUNCT
ejpam-393	851	1	now	now	ADV
ejpam-393	851	2	χm	χm	VERB
ejpam-393	851	3	u	u	PROPN
ejpam-393	851	4	∈	∈	PROPN
ejpam-393	851	5	b	b	PROPN
ejpam-393	851	6	for	for	ADP
ejpam-393	851	7	each	each	DET
ejpam-393	851	8	u	u	PROPN
ejpam-393	851	9	∈	∈	PROPN
ejpam-393	851	10	33	33	NUM
ejpam-393	851	11	.	.	PUNCT
ejpam-393	852	1	identifying	identify	VERB
ejpam-393	852	2	functions	function	NOUN
ejpam-393	852	3	with	with	ADP
ejpam-393	852	4	sequences	sequence	NOUN
ejpam-393	852	5	we	we	PRON
ejpam-393	852	6	let	let	VERB
ejpam-393	852	7	v	v	NOUN
ejpam-393	852	8	=	=	PUNCT
ejpam-393	852	9	〈	〈	NOUN
ejpam-393	852	10	1,0,2	1,0,2	NUM
ejpam-393	852	11	〉	〉	ADJ
ejpam-393	852	12	∈	∈	NOUN
ejpam-393	852	13	33	33	NUM
ejpam-393	852	14	.	.	PUNCT
ejpam-393	853	1	let	let	VERB
ejpam-393	853	2	t(x	t(x	PROPN
ejpam-393	853	3	)	)	PUNCT
ejpam-393	853	4	be	be	VERB
ejpam-393	853	5	the	the	DET
ejpam-393	853	6	ca2	ca2	PROPN
ejpam-393	853	7	term	term	NOUN
ejpam-393	853	8	s0	s0	PROPN
ejpam-393	853	9	1c1	1c1	NUM
ejpam-393	854	1	x	x	SYM
ejpam-393	854	2	.s1	.s1	SYM
ejpam-393	854	3	0c0	0c0	NUM
ejpam-393	855	1	x	x	X
ejpam-393	855	2	,	,	PUNCT
ejpam-393	855	3	where	where	SCONJ
ejpam-393	855	4	s	s	VERB
ejpam-393	855	5	j	j	PROPN
ejpam-393	855	6	i	i	PRON
ejpam-393	855	7	(	(	PUNCT
ejpam-393	855	8	x	x	X
ejpam-393	855	9	)	)	PUNCT
ejpam-393	855	10	=	=	SYM
ejpam-393	856	1	ci(di	ci(di	ADJ
ejpam-393	856	2	j	j	PROPN
ejpam-393	856	3	.x	.x	PROPN
ejpam-393	856	4	)	)	PUNCT
ejpam-393	856	5	,	,	PUNCT
ejpam-393	856	6	for	for	ADP
ejpam-393	856	7	i	i	PRON
ejpam-393	856	8	6=	6=	PROPN
ejpam-393	857	1	j.	j.	PROPN
ejpam-393	857	2	then	then	ADV
ejpam-393	857	3	we	we	PRON
ejpam-393	857	4	claim	claim	VERB
ejpam-393	857	5	that	that	SCONJ
ejpam-393	857	6	tb(χm	tb(χm	PROPN
ejpam-393	857	7	v	v	NOUN
ejpam-393	857	8	)	)	PUNCT
ejpam-393	857	9	=	=	PUNCT
ejpam-393	858	1	χ	χ	NOUN
ejpam-393	858	2	m	m	VERB
ejpam-393	858	3	i	i	NOUN
ejpam-393	858	4	d	d	NOUN
ejpam-393	858	5	.	.	PUNCT
ejpam-393	859	1	for	for	ADP
ejpam-393	859	2	the	the	DET
ejpam-393	859	3	sake	sake	NOUN
ejpam-393	859	4	of	of	ADP
ejpam-393	859	5	brevity	brevity	NOUN
ejpam-393	859	6	,	,	PUNCT
ejpam-393	859	7	denote	denote	VERB
ejpam-393	859	8	χm	χm	NOUN
ejpam-393	859	9	v	v	NOUN
ejpam-393	859	10	by	by	ADP
ejpam-393	859	11	110	110	NUM
ejpam-393	859	12	and	and	CCONJ
ejpam-393	859	13	χm	χm	PRON
ejpam-393	860	1	i	i	PRON
ejpam-393	860	2	d	d	NOUN
ejpam-393	860	3	by	by	ADP
ejpam-393	860	4	101	101	NUM
ejpam-393	860	5	.	.	PUNCT
ejpam-393	861	1	then	then	ADV
ejpam-393	861	2	,	,	PUNCT
ejpam-393	861	3	by	by	ADP
ejpam-393	861	4	definition	definition	NOUN
ejpam-393	861	5	,	,	PUNCT
ejpam-393	861	6	we	we	PRON
ejpam-393	861	7	have	have	AUX
ejpam-393	861	8	tb(101	tb(101	VERB
ejpam-393	861	9	)	)	PUNCT
ejpam-393	861	10	=	=	SYM
ejpam-393	861	11	c0(d01.c1110).c1(d01.c0110	c0(d01.c1110).c1(d01.c0110	NOUN
ejpam-393	861	12	)	)	PUNCT
ejpam-393	861	13	.	.	PUNCT
ejpam-393	862	1	computing	compute	VERB
ejpam-393	862	2	we	we	PRON
ejpam-393	862	3	get	get	VERB
ejpam-393	862	4	c0(d01.c1110	c0(d01.c1110	NOUN
ejpam-393	862	5	)	)	PUNCT
ejpam-393	863	1	=	=	SYM
ejpam-393	863	2	c0(d01	c0(d01	PROPN
ejpam-393	863	3	.	.	PUNCT
ejpam-393	864	1	(	(	PUNCT
ejpam-393	864	2	∑	∑	PUNCT
ejpam-393	864	3	{	{	PUNCT
ejpam-393	864	4	1u	1u	NOUN
ejpam-393	864	5	:	:	PUNCT
ejpam-393	864	6	u≡1	u≡1	NOUN
ejpam-393	864	7	110	110	NUM
ejpam-393	864	8	}	}	PUNCT
ejpam-393	864	9	)	)	PUNCT
ejpam-393	864	10	=	=	SYM
ejpam-393	864	11	c0(d01.1112	c0(d01.1112	ADJ
ejpam-393	864	12	)	)	PUNCT
ejpam-393	864	13	=	=	PUNCT
ejpam-393	865	1	101	101	NUM
ejpam-393	865	2	+	+	NUM
ejpam-393	865	3	1112	1112	NUM
ejpam-393	865	4	.	.	PUNCT
ejpam-393	866	1	here	here	ADV
ejpam-393	866	2	1112	1112	NUM
ejpam-393	866	3	denotes	denote	VERB
ejpam-393	866	4	χ〈1,1,2	χ〈1,1,2	PROPN
ejpam-393	866	5	〉	〉	NOUN
ejpam-393	866	6	.	.	PUNCT
ejpam-393	867	1	note	note	VERB
ejpam-393	867	2	that	that	SCONJ
ejpam-393	867	3	we	we	PRON
ejpam-393	867	4	are	be	AUX
ejpam-393	867	5	using	use	VERB
ejpam-393	867	6	that	that	SCONJ
ejpam-393	867	7	the	the	DET
ejpam-393	867	8	evaluation	evaluation	NOUN
ejpam-393	867	9	of	of	ADP
ejpam-393	867	10	the	the	DET
ejpam-393	867	11	term	term	NOUN
ejpam-393	867	12	c1110	c1110	PROPN
ejpam-393	867	13	in	in	ADP
ejpam-393	867	14	b	b	PROPN
ejpam-393	867	15	is	be	AUX
ejpam-393	867	16	equal	equal	ADJ
ejpam-393	867	17	to	to	ADP
ejpam-393	867	18	its	its	PRON
ejpam-393	867	19	value	value	NOUN
ejpam-393	867	20	in	in	ADP
ejpam-393	867	21	a.	a.	NOUN
ejpam-393	867	22	this	this	PRON
ejpam-393	867	23	is	be	AUX
ejpam-393	867	24	so	so	ADV
ejpam-393	867	25	,	,	PUNCT
ejpam-393	867	26	because	because	SCONJ
ejpam-393	867	27	b	b	NOUN
ejpam-393	867	28	inherits	inherit	VERB
ejpam-393	867	29	the	the	DET
ejpam-393	867	30	interpretation	interpretation	NOUN
ejpam-393	867	31	given	give	VERB
ejpam-393	867	32	to	to	ADP
ejpam-393	867	33	∏	∏	PROPN
ejpam-393	867	34	au	au	PROPN
ejpam-393	867	35	.	.	PUNCT
ejpam-393	868	1	a	a	DET
ejpam-393	868	2	similar	similar	ADJ
ejpam-393	868	3	computation	computation	NOUN
ejpam-393	868	4	gives	give	VERB
ejpam-393	868	5	c1(d01.c0101	c1(d01.c0101	PROPN
ejpam-393	868	6	)	)	PUNCT
ejpam-393	868	7	=	=	PUNCT
ejpam-393	868	8	1002	1002	NUM
ejpam-393	868	9	+	+	CCONJ
ejpam-393	868	10	101	101	NUM
ejpam-393	868	11	,	,	PUNCT
ejpam-393	868	12	where	where	SCONJ
ejpam-393	868	13	1002	1002	NUM
ejpam-393	868	14	denotes	denote	NOUN
ejpam-393	868	15	χ〈0,0,2	χ〈0,0,2	PROPN
ejpam-393	868	16	〉	〉	NOUN
ejpam-393	868	17	.	.	PUNCT
ejpam-393	869	1	therefore	therefore	ADV
ejpam-393	869	2	as	as	SCONJ
ejpam-393	869	3	claimed	claim	VERB
ejpam-393	869	4	tb(110	tb(110	PUNCT
ejpam-393	869	5	)	)	PUNCT
ejpam-393	870	1	=	=	NOUN
ejpam-393	870	2	101	101	NUM
ejpam-393	870	3	.	.	PUNCT
ejpam-393	871	1	now	now	ADV
ejpam-393	871	2	let	let	VERB
ejpam-393	871	3	3s(0,1	3s(0,1	NOUN
ejpam-393	871	4	)	)	PUNCT
ejpam-393	871	5	be	be	AUX
ejpam-393	871	6	the	the	DET
ejpam-393	871	7	unary	unary	ADJ
ejpam-393	871	8	substitution	substitution	NOUN
ejpam-393	871	9	term	term	NOUN
ejpam-393	871	10	as	as	SCONJ
ejpam-393	871	11	defined	define	VERB
ejpam-393	871	12	in	in	ADP
ejpam-393	871	13	[	[	PUNCT
ejpam-393	871	14	11	11	NUM
ejpam-393	871	15	]	]	SYM
ejpam-393	871	16	1.5.12	1.5.12	NUM
ejpam-393	871	17	,	,	PUNCT
ejpam-393	871	18	that	that	PRON
ejpam-393	871	19	is	be	AUX
ejpam-393	871	20	3s(0,1)x	3s(0,1)x	NUM
ejpam-393	871	21	=	=	SYM
ejpam-393	871	22	s3	s3	PROPN
ejpam-393	871	23	0s	0s	NOUN
ejpam-393	871	24	0	0	NUM
ejpam-393	872	1	1s	1s	NUM
ejpam-393	872	2	1	1	NUM
ejpam-393	872	3	3(x	3(x	NUM
ejpam-393	872	4	)	)	PUNCT
ejpam-393	872	5	.	.	PUNCT
ejpam-393	873	1	then	then	ADV
ejpam-393	873	2	for	for	ADP
ejpam-393	873	3	any	any	DET
ejpam-393	873	4	β	β	NOUN
ejpam-393	873	5	>	>	X
ejpam-393	873	6	3	3	NUM
ejpam-393	873	7	we	we	PRON
ejpam-393	873	8	have	have	VERB
ejpam-393	873	9	caβ	caβ	NOUN
ejpam-393	873	10	|=	|=	PUNCT
ejpam-393	873	11	3s(0,1)c3	3s(0,1)c3	NUM
ejpam-393	873	12	x	x	SYM
ejpam-393	873	13	≤	≤	NUM
ejpam-393	873	14	t(c3	t(c3	X
ejpam-393	873	15	x	x	NOUN
ejpam-393	873	16	)	)	PUNCT
ejpam-393	873	17	.	.	PUNCT
ejpam-393	874	1	indeed	indeed	ADV
ejpam-393	874	2	by	by	ADP
ejpam-393	874	3	[	[	X
ejpam-393	874	4	11	11	NUM
ejpam-393	874	5	]	]	SYM
ejpam-393	874	6	1.5.12	1.5.12	NUM
ejpam-393	874	7	,	,	PUNCT
ejpam-393	874	8	1.5.8	1.5.8	NUM
ejpam-393	874	9	and	and	CCONJ
ejpam-393	874	10	1.5.10	1.5.10	NUM
ejpam-393	874	11	(	(	PUNCT
ejpam-393	874	12	ii	ii	NOUN
ejpam-393	874	13	)	)	PUNCT
ejpam-393	874	14	,	,	PUNCT
ejpam-393	874	15	we	we	PRON
ejpam-393	874	16	get	get	VERB
ejpam-393	874	17	3s(0,1)c3x	3s(0,1)c3x	NUM
ejpam-393	874	18	≤	≤	NOUN
ejpam-393	874	19	3s(0,1)c1c3	3s(0,1)c1c3	NUM
ejpam-393	874	20	x	x	X
ejpam-393	875	1	=	=	SYM
ejpam-393	875	2	s3	s3	PROPN
ejpam-393	875	3	0s	0s	NOUN
ejpam-393	875	4	0	0	NUM
ejpam-393	876	1	1s	1s	NUM
ejpam-393	876	2	1	1	NUM
ejpam-393	876	3	3c1c3	3c1c3	NUM
ejpam-393	876	4	x	x	X
ejpam-393	876	5	=	=	SYM
ejpam-393	876	6	s3	s3	PROPN
ejpam-393	876	7	0s	0s	NOUN
ejpam-393	876	8	0	0	NUM
ejpam-393	877	1	1c1c3	1c1c3	NUM
ejpam-393	877	2	x	x	X
ejpam-393	877	3	=	=	SYM
ejpam-393	877	4	s3	s3	PROPN
ejpam-393	877	5	0s	0s	NOUN
ejpam-393	877	6	0	0	NUM
ejpam-393	877	7	1c3c1	1c3c1	NUM
ejpam-393	877	8	x	x	X
ejpam-393	877	9	=	=	SYM
ejpam-393	877	10	s3	s3	PROPN
ejpam-393	877	11	0c3s	0c3s	NOUN
ejpam-393	877	12	0	0	NUM
ejpam-393	878	1	1c1	1c1	NUM
ejpam-393	878	2	x	x	X
ejpam-393	878	3	=	=	SYM
ejpam-393	878	4	c3s	c3s	NOUN
ejpam-393	878	5	0	0	NUM
ejpam-393	878	6	1c1	1c1	NUM
ejpam-393	878	7	x	x	X
ejpam-393	878	8	=	=	SYM
ejpam-393	878	9	s1	s1	NOUN
ejpam-393	878	10	0c1c3	0c1c3	NOUN
ejpam-393	878	11	x	x	X
ejpam-393	878	12	.	.	PUNCT
ejpam-393	879	1	similarly	similarly	ADV
ejpam-393	879	2	3s(0,1)c3x	3s(0,1)c3x	NUM
ejpam-393	879	3	≤	≤	NUM
ejpam-393	879	4	s0	s0	X
ejpam-393	879	5	1c0c3	1c0c3	NUM
ejpam-393	879	6	x	x	SYM
ejpam-393	879	7	therefore	therefore	ADV
ejpam-393	879	8	3s(0,1)c3	3s(0,1)c3	NUM
ejpam-393	879	9	x	x	SYM
ejpam-393	879	10	≤	≤	NUM
ejpam-393	879	11	t(c3	t(c3	X
ejpam-393	879	12	x	x	NOUN
ejpam-393	879	13	)	)	PUNCT
ejpam-393	879	14	.	.	PUNCT
ejpam-393	880	1	it	it	PRON
ejpam-393	880	2	thus	thus	ADV
ejpam-393	880	3	follows	follow	VERB
ejpam-393	880	4	that	that	SCONJ
ejpam-393	880	5	d	d	ADP
ejpam-393	880	6	|=	|=	PUNCT
ejpam-393	880	7	3s(0,1)(χm	3s(0,1)(χm	NUM
ejpam-393	880	8	u	u	NOUN
ejpam-393	880	9	)	)	PUNCT
ejpam-393	880	10	≤	≤	PUNCT
ejpam-393	880	11	s0	s0	PROPN
ejpam-393	880	12	1c1(χ	1c1(χ	NUM
ejpam-393	880	13	m	m	NOUN
ejpam-393	880	14	u	u	NOUN
ejpam-393	880	15	)	)	PUNCT
ejpam-393	880	16	.s	.s	NOUN
ejpam-393	880	17	1	1	NUM
ejpam-393	880	18	0c0(χ	0c0(χ	NUM
ejpam-393	880	19	m	m	NUM
ejpam-393	880	20	u	u	NOUN
ejpam-393	880	21	)	)	PUNCT
ejpam-393	880	22	=	=	PUNCT
ejpam-393	881	1	χ	χ	NOUN
ejpam-393	881	2	m	m	VERB
ejpam-393	881	3	i	i	INTJ
ejpam-393	882	1	d	d	NOUN
ejpam-393	882	2	.	.	PUNCT
ejpam-393	883	1	now	now	ADV
ejpam-393	883	2	3s(0,1	3s(0,1	NOUN
ejpam-393	883	3	)	)	PUNCT
ejpam-393	883	4	preserves	preserve	VERB
ejpam-393	883	5	≤	≤	NUM
ejpam-393	883	6	and	and	CCONJ
ejpam-393	883	7	is	be	AUX
ejpam-393	883	8	one	one	NUM
ejpam-393	883	9	to	to	ADP
ejpam-393	883	10	one	one	NUM
ejpam-393	883	11	nr3d	nr3d	NOUN
ejpam-393	883	12	.	.	PUNCT
ejpam-393	884	1	by	by	ADP
ejpam-393	884	2	[	[	X
ejpam-393	884	3	11	11	NUM
ejpam-393	884	4	]	]	PUNCT
ejpam-393	884	5	,	,	PUNCT
ejpam-393	884	6	1.5.12	1.5.12	NUM
ejpam-393	884	7	and	and	CCONJ
ejpam-393	884	8	1.5.1	1.5.1	NUM
ejpam-393	884	9	,	,	PUNCT
ejpam-393	884	10	we	we	PRON
ejpam-393	884	11	have	have	VERB
ejpam-393	884	12	:	:	PUNCT
ejpam-393	884	13	3s(0,1)c3	3s(0,1)c3	NUM
ejpam-393	884	14	x	x	X
ejpam-393	885	1	=	=	SYM
ejpam-393	885	2	sn	sn	PROPN
ejpam-393	885	3	0s	0s	NOUN
ejpam-393	885	4	0	0	NUM
ejpam-393	886	1	1s	1s	NUM
ejpam-393	886	2	1	1	NUM
ejpam-393	886	3	3c3	3c3	NUM
ejpam-393	886	4	x	x	X
ejpam-393	887	1	=	=	PUNCT
ejpam-393	887	2	c3(d30	c3(d30	PROPN
ejpam-393	887	3	∩	∩	ADJ
ejpam-393	887	4	c0(d01	c0(d01	PROPN
ejpam-393	887	5	∩	∩	ADJ
ejpam-393	887	6	c1(d01	c1(d01	PROPN
ejpam-393	887	7	∩	∩	PROPN
ejpam-393	887	8	c1(d13	c1(d13	PROPN
ejpam-393	887	9	∩	∩	PROPN
ejpam-393	887	10	c3	c3	PROPN
ejpam-393	887	11	x	x	PROPN
ejpam-393	887	12	)	)	PUNCT
ejpam-393	887	13	)	)	PUNCT
ejpam-393	887	14	)	)	PUNCT
ejpam-393	887	15	.	.	PUNCT
ejpam-393	888	1	references	reference	NOUN
ejpam-393	888	2	877	877	NUM
ejpam-393	888	3	by	by	ADP
ejpam-393	888	4	[	[	PUNCT
ejpam-393	888	5	11	11	NUM
ejpam-393	888	6	]	]	PUNCT
ejpam-393	888	7	,	,	PUNCT
ejpam-393	888	8	1.3.8	1.3.8	NUM
ejpam-393	888	9	,	,	PUNCT
ejpam-393	888	10	0	0	NUM
ejpam-393	888	11	<	<	X
ejpam-393	888	12	x	x	X
ejpam-393	888	13	,	,	PUNCT
ejpam-393	888	14	implies	imply	VERB
ejpam-393	888	15	0	0	NUM
ejpam-393	888	16	<	<	X
ejpam-393	888	17	di	di	X
ejpam-393	888	18	j	j	PROPN
ejpam-393	888	19	∩	∩	PROPN
ejpam-393	888	20	c	c	PROPN
ejpam-393	888	21	j	j	PROPN
ejpam-393	888	22	x	x	X
ejpam-393	888	23	,	,	PUNCT
ejpam-393	888	24	for	for	ADP
ejpam-393	888	25	all	all	DET
ejpam-393	888	26	i	i	PROPN
ejpam-393	888	27	,	,	PUNCT
ejpam-393	889	1	j	j	PROPN
ejpam-393	889	2	∈	∈	PROPN
ejpam-393	889	3	β	β	X
ejpam-393	889	4	.	.	PUNCT
ejpam-393	890	1	we	we	PRON
ejpam-393	890	2	have	have	AUX
ejpam-393	890	3	shown	show	VERB
ejpam-393	890	4	that	that	SCONJ
ejpam-393	890	5	if	if	SCONJ
ejpam-393	890	6	x	x	PROPN
ejpam-393	890	7	>	>	X
ejpam-393	890	8	0	0	NUM
ejpam-393	890	9	∈	∈	PROPN
ejpam-393	890	10	n	n	DET
ejpam-393	890	11	r3d	r3d	NOUN
ejpam-393	890	12	,	,	PUNCT
ejpam-393	890	13	then	then	ADV
ejpam-393	890	14	3s(0,1)x	3s(0,1)x	NUM
ejpam-393	890	15	>	>	X
ejpam-393	890	16	0	0	NUM
ejpam-393	890	17	,	,	PUNCT
ejpam-393	890	18	i.e	i.e	CCONJ
ejpam-393	890	19	that	that	DET
ejpam-393	890	20	3s(0,1	3s(0,1	NOUN
ejpam-393	890	21	)	)	PUNCT
ejpam-393	890	22	,	,	PUNCT
ejpam-393	890	23	being	be	AUX
ejpam-393	890	24	a	a	DET
ejpam-393	890	25	boolean	boolean	ADJ
ejpam-393	890	26	endomorphism	endomorphism	NOUN
ejpam-393	890	27	,	,	PUNCT
ejpam-393	890	28	is	be	AUX
ejpam-393	890	29	one	one	NUM
ejpam-393	890	30	to	to	ADP
ejpam-393	890	31	one	one	NUM
ejpam-393	890	32	.	.	PUNCT
ejpam-393	891	1	since	since	SCONJ
ejpam-393	891	2	bv	bv	PROPN
ejpam-393	891	3	=	=	PROPN
ejpam-393	891	4	av	av	PROPN
ejpam-393	891	5	it	it	PRON
ejpam-393	891	6	follows	follow	VERB
ejpam-393	891	7	(	(	PUNCT
ejpam-393	891	8	by	by	ADP
ejpam-393	891	9	condition	condition	NOUN
ejpam-393	891	10	(	(	PUNCT
ejpam-393	891	11	4	4	NUM
ejpam-393	891	12	)	)	PUNCT
ejpam-393	891	13	in	in	ADP
ejpam-393	891	14	lemma	lemma	PROPN
ejpam-393	891	15	13	13	NUM
ejpam-393	891	16	)	)	PUNCT
ejpam-393	891	17	that	that	PRON
ejpam-393	891	18	bv	bv	PROPN
ejpam-393	891	19	=	=	X
ejpam-393	891	20	{	{	PUNCT
ejpam-393	891	21	b	b	PROPN
ejpam-393	891	22	∈	∈	PROPN
ejpam-393	891	23	b	b	PROPN
ejpam-393	891	24	:	:	PUNCT
ejpam-393	891	25	b	b	X
ejpam-393	891	26	≤	≤	NUM
ejpam-393	891	27	χm	χm	PRON
ejpam-393	891	28	v	v	NOUN
ejpam-393	891	29	}	}	PUNCT
ejpam-393	891	30	is	be	AUX
ejpam-393	891	31	uncountable	uncountable	ADJ
ejpam-393	891	32	.	.	PUNCT
ejpam-393	892	1	since	since	SCONJ
ejpam-393	892	2	3s(0,1	3s(0,1	NOUN
ejpam-393	892	3	)	)	PUNCT
ejpam-393	892	4	is	be	AUX
ejpam-393	892	5	one	one	NUM
ejpam-393	892	6	to	to	ADP
ejpam-393	892	7	one	one	NUM
ejpam-393	892	8	,	,	PUNCT
ejpam-393	892	9	it	it	PRON
ejpam-393	892	10	follows	follow	VERB
ejpam-393	892	11	that	that	SCONJ
ejpam-393	892	12	3s(0,1)bu	3s(0,1)bu	PROPN
ejpam-393	892	13	is	be	AUX
ejpam-393	892	14	also	also	ADV
ejpam-393	892	15	uncountable	uncountable	ADJ
ejpam-393	892	16	.	.	PUNCT
ejpam-393	893	1	but	but	CCONJ
ejpam-393	893	2	by	by	ADP
ejpam-393	893	3	the	the	DET
ejpam-393	893	4	above	above	ADV
ejpam-393	893	5	we	we	PRON
ejpam-393	893	6	have	have	AUX
ejpam-393	893	7	3s(0,1)bu	3s(0,1)bu	VERB
ejpam-393	893	8	⊆	⊆	NUM
ejpam-393	893	9	bi	bi	NOUN
ejpam-393	893	10	d	d	PROPN
ejpam-393	893	11	=	=	PUNCT
ejpam-393	893	12	{	{	PUNCT
ejpam-393	893	13	b	b	PROPN
ejpam-393	893	14	∈	∈	PROPN
ejpam-393	893	15	b	b	PROPN
ejpam-393	893	16	:	:	PUNCT
ejpam-393	893	17	b	b	X
ejpam-393	893	18	≤	≤	ADV
ejpam-393	894	1	χb	χb	ADV
ejpam-393	894	2	i	i	PRON
ejpam-393	894	3	d	d	NOUN
ejpam-393	894	4	}	}	PUNCT
ejpam-393	894	5	,	,	PUNCT
ejpam-393	894	6	and	and	CCONJ
ejpam-393	894	7	so	so	ADV
ejpam-393	894	8	bi	bi	PROPN
ejpam-393	894	9	d	d	PROPN
ejpam-393	894	10	is	be	AUX
ejpam-393	894	11	also	also	ADV
ejpam-393	894	12	uncountable	uncountable	ADJ
ejpam-393	894	13	.	.	PUNCT
ejpam-393	895	1	but	but	CCONJ
ejpam-393	895	2	by	by	ADP
ejpam-393	895	3	construction	construction	NOUN
ejpam-393	895	4	,	,	PUNCT
ejpam-393	895	5	we	we	PRON
ejpam-393	895	6	have	have	VERB
ejpam-393	895	7	bi	bi	NOUN
ejpam-393	895	8	d	d	PROPN
ejpam-393	895	9	=	=	PUNCT
ejpam-393	895	10	{	{	PUNCT
ejpam-393	895	11	b	b	PROPN
ejpam-393	895	12	∈	∈	PROPN
ejpam-393	895	13	b	b	PROPN
ejpam-393	895	14	:	:	PUNCT
ejpam-393	896	1	b	b	X
ejpam-393	896	2	≤	≤	NUM
ejpam-393	896	3	χm	χm	VERB
ejpam-393	897	1	i	i	PRON
ejpam-393	897	2	d	d	PROPN
ejpam-393	897	3	}	}	PUNCT
ejpam-393	897	4	is	be	AUX
ejpam-393	897	5	countable	countable	ADJ
ejpam-393	897	6	.	.	PUNCT
ejpam-393	898	1	this	this	DET
ejpam-393	898	2	contradiction	contradiction	NOUN
ejpam-393	898	3	shows	show	VERB
ejpam-393	898	4	that	that	SCONJ
ejpam-393	898	5	b	b	X
ejpam-393	898	6	/∈nr3caβ	/∈nr3caβ	PUNCT
ejpam-393	898	7	for	for	ADP
ejpam-393	898	8	any	any	DET
ejpam-393	898	9	β	β	X
ejpam-393	898	10	>	>	X
ejpam-393	898	11	3	3	X
ejpam-393	898	12	.	.	PUNCT
ejpam-393	899	1	the	the	DET
ejpam-393	899	2	rsc	rsc	PROPN
ejpam-393	899	3	is	be	AUX
ejpam-393	899	4	the	the	DET
ejpam-393	899	5	same	same	ADJ
ejpam-393	899	6	by	by	ADP
ejpam-393	899	7	using	use	VERB
ejpam-393	899	8	the	the	DET
ejpam-393	899	9	axiomatization	axiomatization	NOUN
ejpam-393	899	10	(	(	PUNCT
ejpam-393	899	11	e1	e1	PROPN
ejpam-393	899	12	−	−	PROPN
ejpam-393	899	13	e9	e9	PROPN
ejpam-393	899	14	)	)	PUNCT
ejpam-393	899	15	and	and	CCONJ
ejpam-393	899	16	noting	note	VERB
ejpam-393	899	17	that	that	SCONJ
ejpam-393	899	18	3s(0,1	3s(0,1	NOUN
ejpam-393	899	19	)	)	PUNCT
ejpam-393	899	20	is	be	AUX
ejpam-393	899	21	a	a	DET
ejpam-393	899	22	permutation	permutation	NOUN
ejpam-393	899	23	of	of	ADP
ejpam-393	899	24	nr3d	nr3d	PROPN
ejpam-393	899	25	when	when	SCONJ
ejpam-393	899	26	d	d	PROPN
ejpam-393	899	27	∈	∈	PROPN
ejpam-393	899	28	rsc5	rsc5	NOUN
ejpam-393	899	29	.	.	PUNCT
ejpam-393	900	1	same	same	ADJ
ejpam-393	900	2	reasoning	reasoning	NOUN
ejpam-393	900	3	for	for	ADP
ejpam-393	900	4	scm	scm	PROPN
ejpam-393	900	5	.	.	PUNCT
ejpam-393	901	1	finally	finally	ADV
ejpam-393	901	2	we	we	PRON
ejpam-393	901	3	should	should	AUX
ejpam-393	901	4	mention	mention	VERB
ejpam-393	901	5	that	that	SCONJ
ejpam-393	901	6	the	the	DET
ejpam-393	901	7	proof	proof	NOUN
ejpam-393	901	8	presented	present	VERB
ejpam-393	901	9	herein	herein	NOUN
ejpam-393	901	10	is	be	AUX
ejpam-393	901	11	substantially	substantially	ADV
ejpam-393	901	12	different	different	ADJ
ejpam-393	901	13	than	than	ADP
ejpam-393	901	14	the	the	DET
ejpam-393	901	15	proofs	proof	NOUN
ejpam-393	901	16	in	in	ADP
ejpam-393	901	17	[	[	X
ejpam-393	901	18	21	21	NUM
ejpam-393	901	19	]	]	PUNCT
ejpam-393	901	20	,	,	PUNCT
ejpam-393	902	1	[	[	X
ejpam-393	902	2	18	18	NUM
ejpam-393	902	3	]	]	PUNCT
ejpam-393	902	4	,	,	PUNCT
ejpam-393	903	1	[	[	X
ejpam-393	903	2	34	34	NUM
ejpam-393	903	3	]	]	PUNCT
ejpam-393	903	4	,	,	PUNCT
ejpam-393	903	5	[	[	X
ejpam-393	903	6	29	29	NUM
ejpam-393	903	7	]	]	PUNCT
ejpam-393	903	8	,	,	PUNCT
ejpam-393	903	9	since	since	SCONJ
ejpam-393	903	10	it	it	PRON
ejpam-393	903	11	uses	use	VERB
ejpam-393	903	12	genuine	genuine	ADJ
ejpam-393	903	13	model	model	NOUN
ejpam-393	903	14	theoretic	theoretic	NOUN
ejpam-393	903	15	arguments	argument	NOUN
ejpam-393	903	16	.	.	PUNCT
ejpam-393	904	1	references	reference	NOUN
ejpam-393	904	2	[	[	X
ejpam-393	904	3	1	1	NUM
ejpam-393	904	4	]	]	X
ejpam-393	904	5	h.	h.	PROPN
ejpam-393	904	6	andréka	andréka	PROPN
ejpam-393	904	7	,	,	PUNCT
ejpam-393	904	8	i.	i.	NOUN
ejpam-393	904	9	németi	németi	PROPN
ejpam-393	904	10	,	,	PUNCT
ejpam-393	904	11	t.	t.	PROPN
ejpam-393	904	12	sayed	sayed	PROPN
ejpam-393	904	13	ahmed	ahmed	PROPN
ejpam-393	904	14	,	,	PUNCT
ejpam-393	904	15	omitting	omit	VERB
ejpam-393	904	16	types	type	NOUN
ejpam-393	904	17	for	for	ADP
ejpam-393	904	18	finite	finite	ADJ
ejpam-393	904	19	variable	variable	ADJ
ejpam-393	904	20	fragments	fragment	NOUN
ejpam-393	904	21	and	and	CCONJ
ejpam-393	904	22	complete	complete	ADJ
ejpam-393	904	23	representations	representation	NOUN
ejpam-393	904	24	of	of	ADP
ejpam-393	904	25	algebras	algebras	PROPN
ejpam-393	904	26	.	.	PUNCT
ejpam-393	905	1	journal	journal	PROPN
ejpam-393	905	2	of	of	ADP
ejpam-393	905	3	symbolic	symbolic	ADJ
ejpam-393	905	4	logic	logic	NOUN
ejpam-393	905	5	73(1	73(1	NOUN
ejpam-393	905	6	)	)	PUNCT
ejpam-393	905	7	(	(	PUNCT
ejpam-393	905	8	2008	2008	NUM
ejpam-393	905	9	)	)	PUNCT
ejpam-393	905	10	p.65	p.65	NOUN
ejpam-393	905	11	-	-	SYM
ejpam-393	905	12	89	89	NUM
ejpam-393	906	1	[	[	X
ejpam-393	906	2	2	2	NUM
ejpam-393	906	3	]	]	X
ejpam-393	906	4	h.	h.	PROPN
ejpam-393	906	5	andréka	andréka	PROPN
ejpam-393	906	6	,	,	PUNCT
ejpam-393	906	7	s.givant	s.givant	NOUN
ejpam-393	906	8	,	,	PUNCT
ejpam-393	906	9	s.	s.	PROPN
ejpam-393	906	10	mikulus	mikulus	PROPN
ejpam-393	906	11	,	,	PUNCT
ejpam-393	906	12	i.	i.	NOUN
ejpam-393	906	13	németi	németi	PROPN
ejpam-393	906	14	,	,	PUNCT
ejpam-393	906	15	a.	a.	PROPN
ejpam-393	906	16	simon	simon	PROPN
ejpam-393	906	17	notions	notion	NOUN
ejpam-393	906	18	of	of	ADP
ejpam-393	906	19	density	density	NOUN
ejpam-393	906	20	that	that	PRON
ejpam-393	906	21	imply	imply	VERB
ejpam-393	906	22	representability	representability	NOUN
ejpam-393	906	23	in	in	ADP
ejpam-393	906	24	algebraic	algebraic	ADJ
ejpam-393	906	25	logic	logic	NOUN
ejpam-393	906	26	annals	annal	NOUN
ejpam-393	906	27	of	of	ADP
ejpam-393	906	28	pure	pure	ADJ
ejpam-393	906	29	and	and	CCONJ
ejpam-393	906	30	applied	applied	ADJ
ejpam-393	906	31	logic	logic	NOUN
ejpam-393	906	32	91	91	NUM
ejpam-393	906	33	(	(	PUNCT
ejpam-393	906	34	1998	1998	NUM
ejpam-393	906	35	)	)	PUNCT
ejpam-393	906	36	p.93	p.93	PROPN
ejpam-393	906	37	-	-	SYM
ejpam-393	906	38	190	190	NUM
ejpam-393	906	39	[	[	X
ejpam-393	906	40	3	3	NUM
ejpam-393	906	41	]	]	PUNCT
ejpam-393	906	42	j.	j.	PROPN
ejpam-393	906	43	burgess	burgess	PROPN
ejpam-393	906	44	forcing	force	VERB
ejpam-393	906	45	chapter	chapter	NOUN
ejpam-393	906	46	in	in	ADP
ejpam-393	906	47	handbook	handbook	NOUN
ejpam-393	906	48	of	of	ADP
ejpam-393	906	49	mathemmatical	mathemmatical	ADJ
ejpam-393	906	50	logic	logic	NOUN
ejpam-393	906	51	edited	edit	VERB
ejpam-393	906	52	by	by	ADP
ejpam-393	906	53	barwise	barwise	PROPN
ejpam-393	906	54	.	.	PUNCT
ejpam-393	907	1	j.	j.	PROPN
ejpam-393	908	1	[	[	X
ejpam-393	908	2	4	4	NUM
ejpam-393	908	3	]	]	PUNCT
ejpam-393	908	4	m.	m.	NOUN
ejpam-393	908	5	ferenczi	ferenczi	NOUN
ejpam-393	908	6	,	,	PUNCT
ejpam-393	908	7	on	on	ADP
ejpam-393	908	8	representability	representability	NOUN
ejpam-393	908	9	of	of	ADP
ejpam-393	908	10	neatly	neatly	ADV
ejpam-393	908	11	embeddable	embeddable	ADJ
ejpam-393	908	12	cylindric	cylindric	ADJ
ejpam-393	908	13	algebras	algebras	PROPN
ejpam-393	908	14	journal	journal	PROPN
ejpam-393	908	15	of	of	ADP
ejpam-393	908	16	applied	apply	VERB
ejpam-393	908	17	non	non	ADJ
ejpam-393	908	18	-	-	ADJ
ejpam-393	908	19	classical	classical	ADJ
ejpam-393	908	20	logic	logic	NOUN
ejpam-393	908	21	,	,	PUNCT
ejpam-393	908	22	10	10	NUM
ejpam-393	908	23	3	3	NUM
ejpam-393	908	24	-	-	SYM
ejpam-393	908	25	4(2000	4(2000	NUM
ejpam-393	908	26	)	)	PUNCT
ejpam-393	908	27	,	,	PUNCT
ejpam-393	908	28	p.	p.	NOUN
ejpam-393	908	29	1	1	NUM
ejpam-393	908	30	-	-	SYM
ejpam-393	908	31	11	11	NUM
ejpam-393	909	1	[	[	X
ejpam-393	909	2	5	5	NUM
ejpam-393	909	3	]	]	SYM
ejpam-393	909	4	d	d	NOUN
ejpam-393	909	5	,	,	PUNCT
ejpam-393	909	6	h	h	NOUN
ejpam-393	909	7	,	,	PUNCT
ejpam-393	909	8	fremlin	fremlin	NOUN
ejpam-393	909	9	,	,	PUNCT
ejpam-393	909	10	consequences	consequence	NOUN
ejpam-393	909	11	of	of	ADP
ejpam-393	909	12	ma	ma	PROPN
ejpam-393	909	13	.	.	PROPN
ejpam-393	909	14	cambridge	cambridge	PROPN
ejpam-393	909	15	university	university	PROPN
ejpam-393	909	16	press	press	NOUN
ejpam-393	909	17	.	.	PUNCT
ejpam-393	910	1	(	(	PUNCT
ejpam-393	910	2	1984	1984	NUM
ejpam-393	910	3	)	)	PUNCT
ejpam-393	911	1	[	[	X
ejpam-393	911	2	6	6	NUM
ejpam-393	911	3	]	]	PUNCT
ejpam-393	911	4	w.	w.	PROPN
ejpam-393	911	5	hodges	hodges	PROPN
ejpam-393	911	6	model	model	PROPN
ejpam-393	911	7	theory	theory	PROPN
ejpam-393	911	8	,	,	PUNCT
ejpam-393	911	9	volume	volume	NOUN
ejpam-393	911	10	42	42	NUM
ejpam-393	911	11	of	of	ADP
ejpam-393	911	12	encyclopedia	encyclopedia	NOUN
ejpam-393	911	13	of	of	ADP
ejpam-393	911	14	mathematics	mathematic	NOUN
ejpam-393	911	15	and	and	CCONJ
ejpam-393	911	16	its	its	PRON
ejpam-393	911	17	applications	application	NOUN
ejpam-393	911	18	[	[	X
ejpam-393	911	19	7	7	X
ejpam-393	911	20	]	]	X
ejpam-393	911	21	hirsch	hirsch	PROPN
ejpam-393	911	22	r.	r.	PROPN
ejpam-393	911	23	relation	relation	PROPN
ejpam-393	911	24	algebra	algebra	PROPN
ejpam-393	911	25	reducts	reduct	NOUN
ejpam-393	911	26	of	of	ADP
ejpam-393	911	27	cylindric	cylindric	ADJ
ejpam-393	911	28	algebras	algebra	NOUN
ejpam-393	911	29	and	and	CCONJ
ejpam-393	911	30	complete	complete	ADJ
ejpam-393	911	31	representations	representation	NOUN
ejpam-393	911	32	journal	journal	NOUN
ejpam-393	911	33	of	of	ADP
ejpam-393	911	34	symbolic	symbolic	ADJ
ejpam-393	911	35	logic	logic	NOUN
ejpam-393	911	36	,	,	PUNCT
ejpam-393	911	37	72(2	72(2	NUM
ejpam-393	911	38	)	)	PUNCT
ejpam-393	911	39	(	(	PUNCT
ejpam-393	911	40	2007	2007	NUM
ejpam-393	911	41	)	)	PUNCT
ejpam-393	911	42	p.673	p.673	NOUN
ejpam-393	911	43	-	-	PUNCT
ejpam-393	911	44	703	703	NUM
ejpam-393	911	45	.	.	PUNCT
ejpam-393	912	1	[	[	X
ejpam-393	912	2	8	8	NUM
ejpam-393	912	3	]	]	X
ejpam-393	912	4	r.	r.	PROPN
ejpam-393	912	5	hirsch	hirsch	PROPN
ejpam-393	912	6	and	and	CCONJ
ejpam-393	912	7	i.	i.	PROPN
ejpam-393	912	8	hodkinson	hodkinson	PROPN
ejpam-393	912	9	,	,	PUNCT
ejpam-393	912	10	complete	complete	VERB
ejpam-393	912	11	representations	representation	NOUN
ejpam-393	912	12	in	in	ADP
ejpam-393	912	13	algebraic	algebraic	ADJ
ejpam-393	912	14	logic	logic	NOUN
ejpam-393	912	15	.	.	PUNCT
ejpam-393	913	1	journal	journal	PROPN
ejpam-393	913	2	of	of	ADP
ejpam-393	913	3	symbolic	symbolic	ADJ
ejpam-393	913	4	logic	logic	NOUN
ejpam-393	913	5	,	,	PUNCT
ejpam-393	913	6	62(3	62(3	NOUN
ejpam-393	913	7	)	)	PUNCT
ejpam-393	913	8	(	(	PUNCT
ejpam-393	913	9	1997	1997	NUM
ejpam-393	913	10	)	)	PUNCT
ejpam-393	913	11	,	,	PUNCT
ejpam-393	913	12	816–847	816–847	NUM
ejpam-393	913	13	.	.	PUNCT
ejpam-393	914	1	[	[	X
ejpam-393	914	2	9	9	NUM
ejpam-393	914	3	]	]	PUNCT
ejpam-393	914	4	r.	r.	PROPN
ejpam-393	914	5	hirsch	hirsch	PROPN
ejpam-393	914	6	i.	i.	PROPN
ejpam-393	914	7	hodkinson	hodkinson	PROPN
ejpam-393	914	8	relation	relation	PROPN
ejpam-393	914	9	algebras	algebras	PROPN
ejpam-393	914	10	by	by	ADP
ejpam-393	914	11	games	game	NOUN
ejpam-393	914	12	.	.	PUNCT
ejpam-393	915	1	(	(	PUNCT
ejpam-393	915	2	2002	2002	NUM
ejpam-393	915	3	)	)	PUNCT
ejpam-393	915	4	studies	study	NOUN
ejpam-393	915	5	in	in	ADP
ejpam-393	915	6	logic	logic	NOUN
ejpam-393	915	7	and	and	CCONJ
ejpam-393	915	8	the	the	DET
ejpam-393	915	9	foundations	foundation	NOUN
ejpam-393	915	10	of	of	ADP
ejpam-393	915	11	mathematics	mathematic	NOUN
ejpam-393	915	12	.	.	PUNCT
ejpam-393	916	1	volume	volume	NOUN
ejpam-393	916	2	147	147	NUM
ejpam-393	916	3	.	.	PUNCT
ejpam-393	917	1	(	(	PUNCT
ejpam-393	917	2	2002	2002	NUM
ejpam-393	917	3	)	)	PUNCT
ejpam-393	918	1	[	[	X
ejpam-393	918	2	10	10	NUM
ejpam-393	918	3	]	]	X
ejpam-393	918	4	r.	r.	PROPN
ejpam-393	918	5	hirsch	hirsch	PROPN
ejpam-393	918	6	,	,	PUNCT
ejpam-393	918	7	i.	i.	PROPN
ejpam-393	918	8	hodkinson	hodkinson	PROPN
ejpam-393	918	9	,	,	PUNCT
ejpam-393	918	10	r.	r.	PROPN
ejpam-393	918	11	maddux	maddux	PROPN
ejpam-393	918	12	,	,	PUNCT
ejpam-393	918	13	relation	relation	NOUN
ejpam-393	918	14	algebra	algebra	NOUN
ejpam-393	918	15	reducts	reduct	NOUN
ejpam-393	918	16	of	of	ADP
ejpam-393	918	17	cylindric	cylindric	ADJ
ejpam-393	918	18	algebras	algebra	NOUN
ejpam-393	918	19	and	and	CCONJ
ejpam-393	918	20	an	an	DET
ejpam-393	918	21	application	application	NOUN
ejpam-393	918	22	to	to	ADP
ejpam-393	918	23	proof	proof	NOUN
ejpam-393	918	24	theory	theory	NOUN
ejpam-393	918	25	.	.	PUNCT
ejpam-393	919	1	journal	journal	PROPN
ejpam-393	919	2	of	of	ADP
ejpam-393	919	3	symbolic	symbolic	ADJ
ejpam-393	919	4	logic	logic	NOUN
ejpam-393	919	5	67(1	67(1	NOUN
ejpam-393	919	6	)	)	PUNCT
ejpam-393	919	7	(	(	PUNCT
ejpam-393	919	8	2002	2002	NUM
ejpam-393	919	9	)	)	PUNCT
ejpam-393	919	10	,	,	PUNCT
ejpam-393	919	11	197–213	197–213	NUM
ejpam-393	919	12	.	.	PUNCT
ejpam-393	920	1	[	[	X
ejpam-393	920	2	11	11	NUM
ejpam-393	920	3	]	]	X
ejpam-393	920	4	l.	l.	PROPN
ejpam-393	920	5	henkin	henkin	PROPN
ejpam-393	920	6	,	,	PUNCT
ejpam-393	920	7	j.d	j.d	PROPN
ejpam-393	920	8	.	.	PROPN
ejpam-393	920	9	monk	monk	PROPN
ejpam-393	920	10	and	and	CCONJ
ejpam-393	920	11	a.	a.	NOUN
ejpam-393	920	12	tarski	tarski	PROPN
ejpam-393	920	13	cylindric	cylindric	ADJ
ejpam-393	920	14	algebras	algebras	PROPN
ejpam-393	920	15	part	part	PROPN
ejpam-393	920	16	i.	i.	PROPN
ejpam-393	920	17	north	north	PROPN
ejpam-393	920	18	holland	holland	PROPN
ejpam-393	920	19	,	,	PUNCT
ejpam-393	920	20	(	(	PUNCT
ejpam-393	920	21	1971	1971	NUM
ejpam-393	920	22	.	.	PUNCT
ejpam-393	920	23	)	)	PUNCT
ejpam-393	920	24	references	reference	VERB
ejpam-393	920	25	878	878	NUM
ejpam-393	921	1	[	[	X
ejpam-393	921	2	12	12	NUM
ejpam-393	921	3	]	]	X
ejpam-393	921	4	l.	l.	PROPN
ejpam-393	921	5	henkin	henkin	PROPN
ejpam-393	921	6	,	,	PUNCT
ejpam-393	921	7	j.d	j.d	PROPN
ejpam-393	921	8	.	.	PROPN
ejpam-393	921	9	monk	monk	PROPN
ejpam-393	921	10	,	,	PUNCT
ejpam-393	921	11	and	and	CCONJ
ejpam-393	921	12	a.	a.	NOUN
ejpam-393	921	13	tarski	tarski	PROPN
ejpam-393	921	14	cylindric	cylindric	PROPN
ejpam-393	921	15	algebras	algebras	PROPN
ejpam-393	921	16	part	part	PROPN
ejpam-393	921	17	ii	ii	PROPN
ejpam-393	921	18	.	.	PROPN
ejpam-393	922	1	north	north	PROPN
ejpam-393	922	2	holland	holland	PROPN
ejpam-393	922	3	,	,	PUNCT
ejpam-393	922	4	(	(	PUNCT
ejpam-393	922	5	1985	1985	NUM
ejpam-393	922	6	)	)	PUNCT
ejpam-393	922	7	.	.	PUNCT
ejpam-393	923	1	[	[	X
ejpam-393	923	2	13	13	NUM
ejpam-393	923	3	]	]	X
ejpam-393	923	4	l.	l.	PROPN
ejpam-393	923	5	henkin	henkin	PROPN
ejpam-393	923	6	,	,	PUNCT
ejpam-393	923	7	j.	j.	PROPN
ejpam-393	923	8	d.	d.	PROPN
ejpam-393	923	9	monk	monk	PROPN
ejpam-393	923	10	,	,	PUNCT
ejpam-393	923	11	a.	a.	NOUN
ejpam-393	923	12	tarski	tarski	NOUN
ejpam-393	923	13	,	,	PUNCT
ejpam-393	923	14	h.	h.	PROPN
ejpam-393	923	15	andreka	andreka	PROPN
ejpam-393	923	16	,	,	PUNCT
ejpam-393	923	17	and	and	CCONJ
ejpam-393	923	18	i.	i.	PROPN
ejpam-393	923	19	németi	németi	PROPN
ejpam-393	923	20	,	,	PUNCT
ejpam-393	923	21	cylindric	cylindric	ADJ
ejpam-393	923	22	set	set	NOUN
ejpam-393	923	23	algebras	algebra	NOUN
ejpam-393	923	24	.	.	PUNCT
ejpam-393	924	1	lecture	lecture	NOUN
ejpam-393	924	2	notes	note	NOUN
ejpam-393	924	3	in	in	ADP
ejpam-393	924	4	mathematics	mathematic	NOUN
ejpam-393	924	5	,	,	PUNCT
ejpam-393	924	6	vol	vol	NOUN
ejpam-393	924	7	.	.	PROPN
ejpam-393	924	8	883	883	NUM
ejpam-393	924	9	,	,	PUNCT
ejpam-393	924	10	springer	springer	NOUN
ejpam-393	924	11	-	-	PUNCT
ejpam-393	924	12	verlag	verlag	PROPN
ejpam-393	924	13	,	,	PUNCT
ejpam-393	924	14	berlin	berlin	PROPN
ejpam-393	924	15	,	,	PUNCT
ejpam-393	924	16	(	(	PUNCT
ejpam-393	924	17	1981	1981	NUM
ejpam-393	924	18	)	)	PUNCT
ejpam-393	924	19	,	,	PUNCT
ejpam-393	924	20	p.vi	p.vi	VERB
ejpam-393	924	21	+	+	NOUN
ejpam-393	925	1	323	323	NUM
ejpam-393	925	2	.	.	PUNCT
ejpam-393	926	1	[	[	X
ejpam-393	926	2	14	14	NUM
ejpam-393	926	3	]	]	X
ejpam-393	926	4	i.	i.	NOUN
ejpam-393	926	5	németi	németi	PROPN
ejpam-393	926	6	,	,	PUNCT
ejpam-393	926	7	the	the	DET
ejpam-393	926	8	class	class	NOUN
ejpam-393	926	9	of	of	ADP
ejpam-393	926	10	neat	neat	ADJ
ejpam-393	926	11	reducts	reduct	NOUN
ejpam-393	926	12	of	of	ADP
ejpam-393	926	13	cylindric	cylindric	ADJ
ejpam-393	926	14	algebras	algebra	NOUN
ejpam-393	926	15	is	be	AUX
ejpam-393	926	16	not	not	PART
ejpam-393	926	17	a	a	DET
ejpam-393	926	18	variety	variety	NOUN
ejpam-393	926	19	but	but	CCONJ
ejpam-393	926	20	is	be	AUX
ejpam-393	926	21	closed	close	VERB
ejpam-393	926	22	w.r.t	w.r.t	NOUN
ejpam-393	926	23	.	.	PUNCT
ejpam-393	927	1	hp	hp	PROPN
ejpam-393	927	2	.	.	PROPN
ejpam-393	927	3	notre	notre	PROPN
ejpam-393	927	4	dame	dame	PROPN
ejpam-393	927	5	journal	journal	NOUN
ejpam-393	927	6	of	of	ADP
ejpam-393	927	7	formal	formal	ADJ
ejpam-393	927	8	logic	logic	NOUN
ejpam-393	927	9	,	,	PUNCT
ejpam-393	927	10	24(3	24(3	NUM
ejpam-393	927	11	)	)	PUNCT
ejpam-393	927	12	(	(	PUNCT
ejpam-393	927	13	1983	1983	NUM
ejpam-393	927	14	)	)	PUNCT
ejpam-393	927	15	,	,	PUNCT
ejpam-393	927	16	pp	pp	ADP
ejpam-393	927	17	399	399	NUM
ejpam-393	927	18	-	-	SYM
ejpam-393	927	19	409	409	NUM
ejpam-393	927	20	.	.	PUNCT
ejpam-393	928	1	[	[	X
ejpam-393	928	2	15	15	NUM
ejpam-393	928	3	]	]	X
ejpam-393	928	4	i.	i.	NOUN
ejpam-393	928	5	németi	németi	PROPN
ejpam-393	928	6	,	,	PUNCT
ejpam-393	928	7	algebraisation	algebraisation	NOUN
ejpam-393	928	8	of	of	ADP
ejpam-393	928	9	quantifier	quantifier	NOUN
ejpam-393	928	10	logics	logic	NOUN
ejpam-393	928	11	,	,	PUNCT
ejpam-393	928	12	an	an	DET
ejpam-393	928	13	introductory	introductory	ADJ
ejpam-393	928	14	overview	overview	NOUN
ejpam-393	928	15	.	.	PUNCT
ejpam-393	929	1	math.inst.budapest	math.inst.budapest	ADJ
ejpam-393	929	2	,	,	PUNCT
ejpam-393	929	3	preprint	preprint	NOUN
ejpam-393	929	4	,	,	PUNCT
ejpam-393	929	5	no	no	DET
ejpam-393	929	6	13	13	NUM
ejpam-393	929	7	-	-	SYM
ejpam-393	929	8	1996	1996	NUM
ejpam-393	929	9	.	.	PUNCT
ejpam-393	930	1	a	a	DET
ejpam-393	930	2	shortened	shorten	VERB
ejpam-393	930	3	version	version	NOUN
ejpam-393	930	4	appeared	appear	VERB
ejpam-393	930	5	in	in	ADP
ejpam-393	930	6	studia	studia	PROPN
ejpam-393	930	7	logica	logica	PROPN
ejpam-393	930	8	50(4	50(4	NUM
ejpam-393	930	9	)	)	PUNCT
ejpam-393	930	10	(	(	PUNCT
ejpam-393	930	11	1991)p.465	1991)p.465	NUM
ejpam-393	930	12	-	-	SYM
ejpam-393	930	13	569	569	NUM
ejpam-393	930	14	.	.	PUNCT
ejpam-393	931	1	[	[	X
ejpam-393	931	2	16	16	NUM
ejpam-393	931	3	]	]	X
ejpam-393	931	4	j.	j.	PROPN
ejpam-393	931	5	madárasz	madárasz	PROPN
ejpam-393	931	6	j.	j.	PROPN
ejpam-393	931	7	,	,	PUNCT
ejpam-393	931	8	and	and	CCONJ
ejpam-393	931	9	t.	t.	PROPN
ejpam-393	931	10	sayed	sayed	PROPN
ejpam-393	931	11	ahmed	ahmed	PROPN
ejpam-393	931	12	,	,	PUNCT
ejpam-393	931	13	amalgamation	amalgamation	NOUN
ejpam-393	931	14	,	,	PUNCT
ejpam-393	931	15	interpolation	interpolation	NOUN
ejpam-393	931	16	and	and	CCONJ
ejpam-393	931	17	epimorphisms	epimorphism	NOUN
ejpam-393	931	18	algebra	algebra	NOUN
ejpam-393	931	19	universalis	universali	VERB
ejpam-393	931	20	56	56	NUM
ejpam-393	931	21	(	(	PUNCT
ejpam-393	931	22	2	2	NUM
ejpam-393	931	23	)	)	PUNCT
ejpam-393	931	24	(	(	PUNCT
ejpam-393	931	25	2007	2007	NUM
ejpam-393	931	26	)	)	PUNCT
ejpam-393	932	1	p.	p.	NOUN
ejpam-393	932	2	179	179	NUM
ejpam-393	932	3	-	-	SYM
ejpam-393	932	4	210	210	NUM
ejpam-393	932	5	.	.	PUNCT
ejpam-393	933	1	[	[	X
ejpam-393	933	2	17	17	NUM
ejpam-393	933	3	]	]	PUNCT
ejpam-393	933	4	a.	a.	NOUN
ejpam-393	933	5	miller	miller	PROPN
ejpam-393	933	6	,	,	PUNCT
ejpam-393	933	7	some	some	DET
ejpam-393	933	8	properties	property	NOUN
ejpam-393	933	9	of	of	ADP
ejpam-393	933	10	measure	measure	NOUN
ejpam-393	933	11	and	and	CCONJ
ejpam-393	933	12	category	category	NOUN
ejpam-393	933	13	transactions	transaction	NOUN
ejpam-393	933	14	of	of	ADP
ejpam-393	933	15	the	the	DET
ejpam-393	933	16	american	american	PROPN
ejpam-393	933	17	mathematical	mathematical	PROPN
ejpam-393	933	18	society	society	NOUN
ejpam-393	933	19	,	,	PUNCT
ejpam-393	933	20	266	266	NUM
ejpam-393	933	21	(	(	PUNCT
ejpam-393	933	22	1981	1981	NUM
ejpam-393	933	23	)	)	PUNCT
ejpam-393	933	24	,	,	PUNCT
ejpam-393	933	25	.	.	PUNCT
ejpam-393	934	1	93	93	NUM
ejpam-393	934	2	-	-	SYM
ejpam-393	934	3	113	113	NUM
ejpam-393	934	4	[	[	SYM
ejpam-393	934	5	18	18	NUM
ejpam-393	934	6	]	]	X
ejpam-393	934	7	t.	t.	PROPN
ejpam-393	934	8	sayed	sayed	PROPN
ejpam-393	934	9	ahmed	ahme	VERB
ejpam-393	934	10	the	the	DET
ejpam-393	934	11	class	class	NOUN
ejpam-393	934	12	of	of	ADP
ejpam-393	934	13	neat	neat	ADJ
ejpam-393	934	14	reducts	reduct	NOUN
ejpam-393	934	15	is	be	AUX
ejpam-393	934	16	not	not	PART
ejpam-393	934	17	elementary	elementary	ADJ
ejpam-393	934	18	.	.	PUNCT
ejpam-393	935	1	logic	logic	NOUN
ejpam-393	935	2	journal	journal	PROPN
ejpam-393	935	3	of	of	ADP
ejpam-393	935	4	igpl	igpl	ADJ
ejpam-393	935	5	,	,	PUNCT
ejpam-393	935	6	9	9	NUM
ejpam-393	935	7	(	(	PUNCT
ejpam-393	935	8	2001	2001	NUM
ejpam-393	935	9	)	)	PUNCT
ejpam-393	936	1	p.	p.	NOUN
ejpam-393	936	2	31	31	NUM
ejpam-393	936	3	-	-	SYM
ejpam-393	936	4	65	65	NUM
ejpam-393	936	5	electronically	electronically	ADV
ejpam-393	936	6	available	available	ADJ
ejpam-393	936	7	at	at	ADP
ejpam-393	936	8	http://www.math-inst.hu/pub/algebraiclogic	http://www.math-inst.hu/pub/algebraiclogic	NOUN
ejpam-393	936	9	.	.	PUNCT
ejpam-393	937	1	[	[	X
ejpam-393	937	2	19	19	NUM
ejpam-393	937	3	]	]	X
ejpam-393	937	4	t.	t.	PROPN
ejpam-393	937	5	sayed	sayed	PROPN
ejpam-393	937	6	ahmed	ahmed	PROPN
ejpam-393	937	7	martin	martin	PROPN
ejpam-393	937	8	’s	’s	PART
ejpam-393	937	9	axiom	axiom	NOUN
ejpam-393	937	10	,	,	PUNCT
ejpam-393	937	11	omitting	omit	VERB
ejpam-393	937	12	types	type	NOUN
ejpam-393	937	13	and	and	CCONJ
ejpam-393	937	14	complete	complete	ADJ
ejpam-393	937	15	representations	representation	NOUN
ejpam-393	937	16	in	in	ADP
ejpam-393	937	17	algebraic	algebraic	ADJ
ejpam-393	937	18	logic	logic	NOUN
ejpam-393	937	19	.	.	PUNCT
ejpam-393	938	1	studia	studia	PROPN
ejpam-393	938	2	logica	logica	PROPN
ejpam-393	938	3	72	72	NUM
ejpam-393	938	4	(	(	PUNCT
ejpam-393	938	5	2002	2002	NUM
ejpam-393	938	6	)	)	PUNCT
ejpam-393	938	7	,	,	PUNCT
ejpam-393	938	8	p.1	p.1	NOUN
ejpam-393	938	9	-	-	SYM
ejpam-393	938	10	25	25	NUM
ejpam-393	938	11	[	[	SYM
ejpam-393	938	12	20	20	NUM
ejpam-393	938	13	]	]	X
ejpam-393	938	14	t.	t.	PROPN
ejpam-393	938	15	sayed	sayed	PROPN
ejpam-393	938	16	ahmed	ahmed	PROPN
ejpam-393	938	17	neat	neat	ADJ
ejpam-393	938	18	embeddings	embedding	NOUN
ejpam-393	938	19	,	,	PUNCT
ejpam-393	938	20	interpolation	interpolation	NOUN
ejpam-393	938	21	,	,	PUNCT
ejpam-393	938	22	and	and	CCONJ
ejpam-393	938	23	omitting	omit	VERB
ejpam-393	938	24	types	type	NOUN
ejpam-393	938	25	,	,	PUNCT
ejpam-393	938	26	an	an	DET
ejpam-393	938	27	overview	overview	NOUN
ejpam-393	938	28	.	.	PUNCT
ejpam-393	939	1	notre	notre	PROPN
ejpam-393	939	2	dame	dame	PROPN
ejpam-393	939	3	journal	journal	NOUN
ejpam-393	939	4	of	of	ADP
ejpam-393	939	5	formal	formal	ADJ
ejpam-393	939	6	logic	logic	NOUN
ejpam-393	939	7	,	,	PUNCT
ejpam-393	939	8	44	44	NUM
ejpam-393	939	9	(	(	PUNCT
ejpam-393	939	10	3)(2003	3)(2003	NUM
ejpam-393	939	11	)	)	PUNCT
ejpam-393	939	12	,	,	PUNCT
ejpam-393	939	13	p.157	p.157	PROPN
ejpam-393	939	14	-	-	NOUN
ejpam-393	939	15	173	173	NUM
ejpam-393	940	1	[	[	X
ejpam-393	940	2	21	21	NUM
ejpam-393	940	3	]	]	X
ejpam-393	940	4	t.	t.	PROPN
ejpam-393	940	5	sayed	sayed	PROPN
ejpam-393	940	6	ahmed	ahmed	PROPN
ejpam-393	940	7	,	,	PUNCT
ejpam-393	940	8	the	the	DET
ejpam-393	940	9	class	class	NOUN
ejpam-393	940	10	of	of	ADP
ejpam-393	940	11	2	2	NUM
ejpam-393	940	12	-	-	PUNCT
ejpam-393	940	13	dimensional	dimensional	ADJ
ejpam-393	940	14	neat	neat	ADJ
ejpam-393	940	15	reducts	reduct	NOUN
ejpam-393	940	16	of	of	ADP
ejpam-393	940	17	polyadic	polyadic	ADJ
ejpam-393	940	18	algebras	algebra	NOUN
ejpam-393	940	19	is	be	AUX
ejpam-393	940	20	not	not	PART
ejpam-393	940	21	elementary	elementary	ADJ
ejpam-393	940	22	.	.	PUNCT
ejpam-393	941	1	fundementa	fundementa	PROPN
ejpam-393	941	2	mathematicea	mathematicea	PROPN
ejpam-393	941	3	,	,	PUNCT
ejpam-393	941	4	172	172	NUM
ejpam-393	941	5	(	(	PUNCT
ejpam-393	941	6	2002	2002	NUM
ejpam-393	941	7	)	)	PUNCT
ejpam-393	941	8	,	,	PUNCT
ejpam-393	941	9	p.61	p.61	NOUN
ejpam-393	941	10	-	-	PUNCT
ejpam-393	941	11	81	81	NUM
ejpam-393	941	12	.	.	PUNCT
ejpam-393	942	1	[	[	X
ejpam-393	942	2	22	22	NUM
ejpam-393	942	3	]	]	X
ejpam-393	942	4	t.	t.	PROPN
ejpam-393	942	5	sayed	sayed	PROPN
ejpam-393	942	6	ahmed	ahmed	PROPN
ejpam-393	942	7	,	,	PUNCT
ejpam-393	942	8	martin	martin	PROPN
ejpam-393	942	9	’s	’s	PART
ejpam-393	942	10	axiom	axiom	NOUN
ejpam-393	942	11	,	,	PUNCT
ejpam-393	942	12	omitting	omit	VERB
ejpam-393	942	13	types	type	NOUN
ejpam-393	942	14	and	and	CCONJ
ejpam-393	942	15	complete	complete	ADJ
ejpam-393	942	16	representations	representation	NOUN
ejpam-393	942	17	in	in	ADP
ejpam-393	942	18	algebraic	algebraic	ADJ
ejpam-393	942	19	logic	logic	NOUN
ejpam-393	942	20	.	.	PUNCT
ejpam-393	943	1	studia	studia	PROPN
ejpam-393	943	2	logica	logica	PROPN
ejpam-393	943	3	72	72	NUM
ejpam-393	943	4	(	(	PUNCT
ejpam-393	943	5	2002	2002	NUM
ejpam-393	943	6	)	)	PUNCT
ejpam-393	943	7	,	,	PUNCT
ejpam-393	943	8	p.1	p.1	NOUN
ejpam-393	943	9	-	-	SYM
ejpam-393	943	10	25	25	NUM
ejpam-393	944	1	[	[	X
ejpam-393	944	2	23	23	NUM
ejpam-393	944	3	]	]	X
ejpam-393	944	4	t.	t.	PROPN
ejpam-393	944	5	sayed	sayed	PROPN
ejpam-393	944	6	ahmed	ahmed	PROPN
ejpam-393	944	7	,	,	PUNCT
ejpam-393	944	8	a	a	DET
ejpam-393	944	9	confirmation	confirmation	NOUN
ejpam-393	944	10	of	of	ADP
ejpam-393	944	11	a	a	DET
ejpam-393	944	12	conjecture	conjecture	NOUN
ejpam-393	944	13	of	of	ADP
ejpam-393	944	14	tarski	tarski	ADJ
ejpam-393	944	15	bulletin	bulletin	NOUN
ejpam-393	944	16	section	section	NOUN
ejpam-393	944	17	of	of	ADP
ejpam-393	944	18	logic	logic	NOUN
ejpam-393	944	19	32	32	NUM
ejpam-393	944	20	(	(	PUNCT
ejpam-393	944	21	3	3	NUM
ejpam-393	944	22	)	)	PUNCT
ejpam-393	944	23	(	(	PUNCT
ejpam-393	944	24	2003	2003	NUM
ejpam-393	944	25	)	)	PUNCT
ejpam-393	944	26	,	,	PUNCT
ejpam-393	944	27	p.103	p.103	NOUN
ejpam-393	944	28	-	-	SYM
ejpam-393	944	29	105	105	NUM
ejpam-393	944	30	[	[	X
ejpam-393	944	31	24	24	NUM
ejpam-393	944	32	]	]	X
ejpam-393	944	33	t.	t.	PROPN
ejpam-393	944	34	sayed	sayed	PROPN
ejpam-393	944	35	ahmed	ahmed	PROPN
ejpam-393	944	36	,	,	PUNCT
ejpam-393	944	37	neat	neat	ADJ
ejpam-393	944	38	embeddings	embedding	NOUN
ejpam-393	944	39	,	,	PUNCT
ejpam-393	944	40	interpolation	interpolation	NOUN
ejpam-393	944	41	,	,	PUNCT
ejpam-393	944	42	and	and	CCONJ
ejpam-393	944	43	omitting	omit	VERB
ejpam-393	944	44	types	type	NOUN
ejpam-393	944	45	,	,	PUNCT
ejpam-393	944	46	an	an	DET
ejpam-393	944	47	overview	overview	NOUN
ejpam-393	944	48	.	.	PUNCT
ejpam-393	945	1	notre	notre	PROPN
ejpam-393	945	2	dame	dame	PROPN
ejpam-393	945	3	journal	journal	NOUN
ejpam-393	945	4	of	of	ADP
ejpam-393	945	5	formal	formal	ADJ
ejpam-393	945	6	logic	logic	NOUN
ejpam-393	945	7	,	,	PUNCT
ejpam-393	945	8	44	44	NUM
ejpam-393	945	9	(	(	PUNCT
ejpam-393	945	10	3)(2003	3)(2003	NUM
ejpam-393	945	11	)	)	PUNCT
ejpam-393	945	12	,	,	PUNCT
ejpam-393	945	13	p.157	p.157	PROPN
ejpam-393	945	14	-	-	NOUN
ejpam-393	945	15	173	173	NUM
ejpam-393	946	1	[	[	X
ejpam-393	946	2	25	25	NUM
ejpam-393	946	3	]	]	PUNCT
ejpam-393	946	4	t.	t.	PROPN
ejpam-393	946	5	sayed	sayed	PROPN
ejpam-393	946	6	ahmed	ahmed	PROPN
ejpam-393	946	7	,	,	PUNCT
ejpam-393	946	8	on	on	ADP
ejpam-393	946	9	amalgamation	amalgamation	NOUN
ejpam-393	946	10	of	of	ADP
ejpam-393	946	11	reducts	reduct	NOUN
ejpam-393	946	12	of	of	ADP
ejpam-393	946	13	polyadic	polyadic	ADJ
ejpam-393	946	14	algebras	algebra	NOUN
ejpam-393	946	15	.	.	PUNCT
ejpam-393	947	1	algebra	algebra	PROPN
ejpam-393	947	2	universalis	universali	VERB
ejpam-393	947	3	51	51	NUM
ejpam-393	947	4	(	(	PUNCT
ejpam-393	947	5	2004	2004	NUM
ejpam-393	947	6	)	)	PUNCT
ejpam-393	947	7	,	,	PUNCT
ejpam-393	947	8	p.301	p.301	NOUN
ejpam-393	947	9	-	-	SYM
ejpam-393	947	10	359	359	NUM
ejpam-393	947	11	.	.	PUNCT
ejpam-393	948	1	[	[	X
ejpam-393	948	2	26	26	NUM
ejpam-393	948	3	]	]	X
ejpam-393	948	4	t.	t.	PROPN
ejpam-393	948	5	sayed	sayed	PROPN
ejpam-393	948	6	ahmed	ahmed	PROPN
ejpam-393	948	7	,	,	PUNCT
ejpam-393	948	8	on	on	ADP
ejpam-393	948	9	amalgamation	amalgamation	NOUN
ejpam-393	948	10	of	of	ADP
ejpam-393	948	11	algebras	algebra	NOUN
ejpam-393	948	12	of	of	ADP
ejpam-393	948	13	logic	logic	NOUN
ejpam-393	948	14	studia	studia	PROPN
ejpam-393	948	15	logica	logica	PROPN
ejpam-393	948	16	81	81	NUM
ejpam-393	948	17	(	(	PUNCT
ejpam-393	948	18	2005	2005	NUM
ejpam-393	948	19	)	)	PUNCT
ejpam-393	948	20	,	,	PUNCT
ejpam-393	948	21	p.6177	p.6177	NOUN
ejpam-393	948	22	.	.	PUNCT
ejpam-393	949	1	[	[	X
ejpam-393	949	2	27	27	NUM
ejpam-393	949	3	]	]	X
ejpam-393	949	4	t.	t.	PROPN
ejpam-393	949	5	sayed	sayed	PROPN
ejpam-393	949	6	ahmed	ahmed	PROPN
ejpam-393	949	7	,	,	PUNCT
ejpam-393	949	8	algebraic	algebraic	ADJ
ejpam-393	949	9	logic	logic	NOUN
ejpam-393	949	10	,	,	PUNCT
ejpam-393	949	11	where	where	SCONJ
ejpam-393	949	12	does	do	AUX
ejpam-393	949	13	it	it	PRON
ejpam-393	949	14	stand	stand	VERB
ejpam-393	949	15	today	today	NOUN
ejpam-393	949	16	?	?	PUNCT
ejpam-393	950	1	bulletin	bulletin	NOUN
ejpam-393	950	2	of	of	ADP
ejpam-393	950	3	symbolic	symbolic	ADJ
ejpam-393	950	4	logic	logic	NOUN
ejpam-393	950	5	.	.	PUNCT
ejpam-393	951	1	11	11	NUM
ejpam-393	951	2	(	(	PUNCT
ejpam-393	951	3	4	4	NUM
ejpam-393	951	4	)	)	PUNCT
ejpam-393	951	5	(	(	PUNCT
ejpam-393	951	6	2005	2005	NUM
ejpam-393	951	7	)	)	PUNCT
ejpam-393	951	8	,	,	PUNCT
ejpam-393	951	9	p.465	p.465	NOUN
ejpam-393	951	10	-	-	PUNCT
ejpam-393	951	11	516	516	NUM
ejpam-393	951	12	.	.	PUNCT
ejpam-393	951	13	references	reference	NOUN
ejpam-393	951	14	879	879	NUM
ejpam-393	951	15	[	[	X
ejpam-393	951	16	28	28	NUM
ejpam-393	951	17	]	]	X
ejpam-393	951	18	t.	t.	PROPN
ejpam-393	951	19	sayed	sayed	PROPN
ejpam-393	951	20	ahmed	ahmed	PROPN
ejpam-393	951	21	,	,	PUNCT
ejpam-393	951	22	the	the	DET
ejpam-393	951	23	class	class	NOUN
ejpam-393	951	24	of	of	ADP
ejpam-393	951	25	infinite	infinite	ADJ
ejpam-393	951	26	dimensional	dimensional	ADJ
ejpam-393	951	27	neat	neat	ADJ
ejpam-393	951	28	reducts	reduct	NOUN
ejpam-393	951	29	quasi	quasi	ADJ
ejpam-393	951	30	-	-	NOUN
ejpam-393	951	31	polyadic	polyadic	ADJ
ejpam-393	951	32	algebras	algebras	PROPN
ejpam-393	951	33	is	be	AUX
ejpam-393	951	34	not	not	PART
ejpam-393	951	35	axiomatizable	axiomatizable	ADJ
ejpam-393	951	36	mathematical	mathematical	ADJ
ejpam-393	951	37	logic	logic	NOUN
ejpam-393	951	38	quaterly	quaterly	ADV
ejpam-393	951	39	52	52	NUM
ejpam-393	951	40	(	(	PUNCT
ejpam-393	951	41	1	1	NUM
ejpam-393	951	42	)	)	PUNCT
ejpam-393	951	43	(	(	PUNCT
ejpam-393	951	44	2006	2006	NUM
ejpam-393	951	45	)	)	PUNCT
ejpam-393	951	46	,	,	PUNCT
ejpam-393	951	47	p.106	p.106	NOUN
ejpam-393	951	48	-	-	PUNCT
ejpam-393	951	49	112	112	NUM
ejpam-393	951	50	[	[	X
ejpam-393	951	51	29	29	NUM
ejpam-393	951	52	]	]	PUNCT
ejpam-393	951	53	t.sayed	t.saye	VERB
ejpam-393	951	54	ahmed	ahme	VERB
ejpam-393	951	55	a	a	DET
ejpam-393	951	56	note	note	NOUN
ejpam-393	951	57	on	on	ADP
ejpam-393	951	58	neat	neat	ADJ
ejpam-393	951	59	reducts	reduct	NOUN
ejpam-393	951	60	,	,	PUNCT
ejpam-393	951	61	studia	studia	PROPN
ejpam-393	951	62	logica	logica	PROPN
ejpam-393	951	63	85(2	85(2	NUM
ejpam-393	951	64	)	)	PUNCT
ejpam-393	951	65	,	,	PUNCT
ejpam-393	951	66	(	(	PUNCT
ejpam-393	951	67	2007)p	2007)p	NUM
ejpam-393	951	68	.	.	NOUN
ejpam-393	951	69	139	139	NUM
ejpam-393	951	70	-	-	SYM
ejpam-393	951	71	151	151	NUM
ejpam-393	951	72	.	.	PUNCT
ejpam-393	952	1	[	[	X
ejpam-393	952	2	30	30	NUM
ejpam-393	952	3	]	]	X
ejpam-393	952	4	t.	t.	PROPN
ejpam-393	952	5	sayed	sayed	PROPN
ejpam-393	952	6	ahmed	ahmed	PROPN
ejpam-393	952	7	on	on	ADP
ejpam-393	952	8	amalgamation	amalgamation	NOUN
ejpam-393	952	9	of	of	ADP
ejpam-393	952	10	reducts	reduct	NOUN
ejpam-393	952	11	of	of	ADP
ejpam-393	952	12	polyadic	polyadic	ADJ
ejpam-393	952	13	algebras	algebra	NOUN
ejpam-393	952	14	.	.	PUNCT
ejpam-393	953	1	algebra	algebra	PROPN
ejpam-393	953	2	universalis	universali	VERB
ejpam-393	953	3	51	51	NUM
ejpam-393	953	4	(	(	PUNCT
ejpam-393	953	5	2004	2004	NUM
ejpam-393	953	6	)	)	PUNCT
ejpam-393	953	7	,	,	PUNCT
ejpam-393	953	8	p.301	p.301	NOUN
ejpam-393	953	9	-	-	SYM
ejpam-393	953	10	359	359	NUM
ejpam-393	953	11	.	.	PUNCT
ejpam-393	954	1	[	[	X
ejpam-393	954	2	31	31	NUM
ejpam-393	954	3	]	]	PUNCT
ejpam-393	954	4	t.	t.	PROPN
ejpam-393	954	5	sayed	sayed	PROPN
ejpam-393	954	6	ahmed	ahmed	PROPN
ejpam-393	954	7	,	,	PUNCT
ejpam-393	954	8	amalgamation	amalgamation	NOUN
ejpam-393	954	9	theorems	theorem	NOUN
ejpam-393	954	10	in	in	ADP
ejpam-393	954	11	algebraic	algebraic	ADJ
ejpam-393	954	12	logic	logic	NOUN
ejpam-393	954	13	,	,	PUNCT
ejpam-393	954	14	an	an	DET
ejpam-393	954	15	overview	overview	NOUN
ejpam-393	954	16	logic	logic	NOUN
ejpam-393	954	17	journal	journal	NOUN
ejpam-393	954	18	of	of	ADP
ejpam-393	954	19	igpl	igpl	ADJ
ejpam-393	954	20	,	,	PUNCT
ejpam-393	954	21	13	13	NUM
ejpam-393	954	22	(	(	PUNCT
ejpam-393	954	23	2005	2005	NUM
ejpam-393	954	24	)	)	PUNCT
ejpam-393	954	25	,	,	PUNCT
ejpam-393	954	26	277	277	NUM
ejpam-393	954	27	-	-	SYM
ejpam-393	954	28	286	286	NUM
ejpam-393	954	29	.	.	PUNCT
ejpam-393	955	1	[	[	X
ejpam-393	955	2	32	32	NUM
ejpam-393	955	3	]	]	PUNCT
ejpam-393	955	4	t.	t.	PROPN
ejpam-393	955	5	sayed	sayed	PROPN
ejpam-393	955	6	ahmed	ahmed	PROPN
ejpam-393	955	7	,	,	PUNCT
ejpam-393	955	8	on	on	ADP
ejpam-393	955	9	amalgamation	amalgamation	NOUN
ejpam-393	955	10	of	of	ADP
ejpam-393	955	11	algebras	algebra	NOUN
ejpam-393	955	12	of	of	ADP
ejpam-393	955	13	logic	logic	NOUN
ejpam-393	955	14	studia	studia	PROPN
ejpam-393	955	15	logica	logica	PROPN
ejpam-393	955	16	81	81	NUM
ejpam-393	955	17	(	(	PUNCT
ejpam-393	955	18	2005	2005	NUM
ejpam-393	955	19	)	)	PUNCT
ejpam-393	955	20	,	,	PUNCT
ejpam-393	955	21	p.6177	p.6177	NOUN
ejpam-393	955	22	.	.	PUNCT
ejpam-393	956	1	[	[	X
ejpam-393	956	2	33	33	NUM
ejpam-393	956	3	]	]	PUNCT
ejpam-393	956	4	t.	t.	PROPN
ejpam-393	956	5	sayed	sayed	PROPN
ejpam-393	956	6	ahmed	ahmed	PROPN
ejpam-393	956	7	,	,	PUNCT
ejpam-393	956	8	algebraic	algebraic	ADJ
ejpam-393	956	9	logic	logic	NOUN
ejpam-393	956	10	,	,	PUNCT
ejpam-393	956	11	where	where	SCONJ
ejpam-393	956	12	does	do	AUX
ejpam-393	956	13	it	it	PRON
ejpam-393	956	14	stand	stand	VERB
ejpam-393	956	15	today	today	NOUN
ejpam-393	956	16	?	?	PUNCT
ejpam-393	957	1	bulletin	bulletin	NOUN
ejpam-393	957	2	of	of	ADP
ejpam-393	957	3	symbolic	symbolic	ADJ
ejpam-393	957	4	logic	logic	NOUN
ejpam-393	957	5	.	.	PUNCT
ejpam-393	958	1	11	11	NUM
ejpam-393	958	2	(	(	PUNCT
ejpam-393	958	3	4	4	NUM
ejpam-393	958	4	)	)	PUNCT
ejpam-393	958	5	(	(	PUNCT
ejpam-393	958	6	2005	2005	NUM
ejpam-393	958	7	)	)	PUNCT
ejpam-393	958	8	,	,	PUNCT
ejpam-393	958	9	p.465	p.465	NOUN
ejpam-393	958	10	-	-	PUNCT
ejpam-393	958	11	516	516	NUM
ejpam-393	958	12	.	.	PUNCT
ejpam-393	959	1	[	[	X
ejpam-393	959	2	34	34	NUM
ejpam-393	959	3	]	]	X
ejpam-393	959	4	t.	t.	PROPN
ejpam-393	959	5	sayed	sayed	PROPN
ejpam-393	959	6	ahmed	ahmed	PROPN
ejpam-393	959	7	,	,	PUNCT
ejpam-393	959	8	the	the	DET
ejpam-393	959	9	class	class	NOUN
ejpam-393	959	10	of	of	ADP
ejpam-393	959	11	infinite	infinite	ADJ
ejpam-393	959	12	dimensional	dimensional	ADJ
ejpam-393	959	13	neat	neat	ADJ
ejpam-393	959	14	reducts	reduct	NOUN
ejpam-393	959	15	of	of	ADP
ejpam-393	959	16	quasi	quasi	ADJ
ejpam-393	959	17	-	-	ADJ
ejpam-393	959	18	polyadic	polyadic	ADJ
ejpam-393	959	19	algebras	algebras	PROPN
ejpam-393	959	20	is	be	AUX
ejpam-393	959	21	not	not	PART
ejpam-393	959	22	axiomatizable	axiomatizable	ADJ
ejpam-393	959	23	mathematical	mathematical	ADJ
ejpam-393	959	24	logic	logic	NOUN
ejpam-393	959	25	quaterly	quaterly	ADV
ejpam-393	959	26	52	52	NUM
ejpam-393	959	27	(	(	PUNCT
ejpam-393	959	28	1	1	NUM
ejpam-393	959	29	)	)	PUNCT
ejpam-393	959	30	(	(	PUNCT
ejpam-393	959	31	2006	2006	NUM
ejpam-393	959	32	)	)	PUNCT
ejpam-393	959	33	,	,	PUNCT
ejpam-393	959	34	p.106	p.106	NOUN
ejpam-393	959	35	-	-	PUNCT
ejpam-393	959	36	112	112	NUM
ejpam-393	960	1	[	[	X
ejpam-393	960	2	35	35	NUM
ejpam-393	960	3	]	]	X
ejpam-393	960	4	t.	t.	PROPN
ejpam-393	960	5	sayed	sayed	PROPN
ejpam-393	960	6	ahmed	ahmed	PROPN
ejpam-393	960	7	,	,	PUNCT
ejpam-393	960	8	omitting	omit	VERB
ejpam-393	960	9	types	type	NOUN
ejpam-393	960	10	for	for	ADP
ejpam-393	960	11	algebraizable	algebraizable	ADJ
ejpam-393	960	12	extensions	extension	NOUN
ejpam-393	960	13	of	of	ADP
ejpam-393	960	14	first	first	ADJ
ejpam-393	960	15	order	order	NOUN
ejpam-393	960	16	logic	logic	NOUN
ejpam-393	960	17	journal	journal	NOUN
ejpam-393	960	18	of	of	ADP
ejpam-393	960	19	applied	apply	VERB
ejpam-393	960	20	non	non	ADJ
ejpam-393	960	21	-	-	ADJ
ejpam-393	960	22	classical	classical	ADJ
ejpam-393	960	23	logics	logic	NOUN
ejpam-393	960	24	15	15	NUM
ejpam-393	960	25	(	(	PUNCT
ejpam-393	960	26	4	4	NUM
ejpam-393	960	27	)	)	PUNCT
ejpam-393	960	28	(	(	PUNCT
ejpam-393	960	29	2006	2006	NUM
ejpam-393	960	30	)	)	PUNCT
ejpam-393	960	31	,	,	PUNCT
ejpam-393	960	32	p.465	p.465	NOUN
ejpam-393	960	33	-	-	PUNCT
ejpam-393	960	34	487	487	NUM
ejpam-393	961	1	[	[	X
ejpam-393	961	2	36	36	NUM
ejpam-393	961	3	]	]	PUNCT
ejpam-393	961	4	t.sayed	t.saye	VERB
ejpam-393	961	5	ahmed	ahmed	PROPN
ejpam-393	961	6	non	non	PROPN
ejpam-393	961	7	elementary	elementary	PROPN
ejpam-393	961	8	classes	class	NOUN
ejpam-393	961	9	in	in	ADP
ejpam-393	961	10	algebraic	algebraic	ADJ
ejpam-393	961	11	logic	logic	NOUN
ejpam-393	961	12	submitted	submit	VERB
ejpam-393	961	13	[	[	X
ejpam-393	961	14	37	37	NUM
ejpam-393	961	15	]	]	PUNCT
ejpam-393	961	16	t.	t.	PROPN
ejpam-393	961	17	sayed	sayed	PROPN
ejpam-393	961	18	ahmed	ahmed	PROPN
ejpam-393	961	19	.	.	PUNCT
ejpam-393	962	1	on	on	ADP
ejpam-393	962	2	a	a	DET
ejpam-393	962	3	theorem	theorem	NOUN
ejpam-393	962	4	of	of	ADP
ejpam-393	962	5	vaught	vaught	PROPN
ejpam-393	962	6	for	for	ADP
ejpam-393	962	7	first	first	ADJ
ejpam-393	962	8	order	order	NOUN
ejpam-393	962	9	logic	logic	NOUN
ejpam-393	962	10	with	with	ADP
ejpam-393	962	11	finitely	finitely	ADV
ejpam-393	962	12	many	many	ADJ
ejpam-393	962	13	variables	variable	NOUN
ejpam-393	962	14	journal	journal	NOUN
ejpam-393	962	15	of	of	ADP
ejpam-393	962	16	applied	apply	VERB
ejpam-393	962	17	non	non	ADJ
ejpam-393	962	18	-	-	ADJ
ejpam-393	962	19	classical	classical	ADJ
ejpam-393	962	20	logic	logic	NOUN
ejpam-393	962	21	19(1	19(1	NUM
ejpam-393	962	22	)	)	PUNCT
ejpam-393	962	23	(	(	PUNCT
ejpam-393	962	24	2009	2009	NUM
ejpam-393	962	25	)	)	PUNCT
ejpam-393	963	1	p.	p.	NOUN
ejpam-393	963	2	97	97	NUM
ejpam-393	963	3	-	-	SYM
ejpam-393	963	4	112	112	NUM
ejpam-393	963	5	.	.	PUNCT
ejpam-393	964	1	[	[	X
ejpam-393	964	2	38	38	NUM
ejpam-393	964	3	]	]	PUNCT
ejpam-393	964	4	t.	t.	PROPN
ejpam-393	964	5	sayed	sayed	PROPN
ejpam-393	964	6	ahmed	ahmed	PROPN
ejpam-393	964	7	.	.	PUNCT
ejpam-393	965	1	a	a	DET
ejpam-393	965	2	note	note	NOUN
ejpam-393	965	3	on	on	ADP
ejpam-393	965	4	substitutions	substitution	NOUN
ejpam-393	965	5	in	in	ADP
ejpam-393	965	6	cylindric	cylindric	ADJ
ejpam-393	965	7	algebras	algebras	PROPN
ejpam-393	965	8	mathematical	mathematical	ADJ
ejpam-393	965	9	logic	logic	NOUN
ejpam-393	965	10	quarterly	quarterly	NOUN
ejpam-393	965	11	55(3)(2009	55(3)(2009	NUM
ejpam-393	965	12	)	)	PUNCT
ejpam-393	965	13	p.	p.	NOUN
ejpam-393	965	14	280	280	NUM
ejpam-393	965	15	-	-	SYM
ejpam-393	965	16	287	287	NUM
ejpam-393	965	17	[	[	X
ejpam-393	965	18	39	39	NUM
ejpam-393	965	19	]	]	PUNCT
ejpam-393	965	20	t.	t.	PROPN
ejpam-393	965	21	sayed	sayed	PROPN
ejpam-393	965	22	ahmed	ahme	VERB
ejpam-393	965	23	on	on	ADP
ejpam-393	965	24	neat	neat	ADJ
ejpam-393	965	25	embeddings	embedding	NOUN
ejpam-393	965	26	of	of	ADP
ejpam-393	965	27	cylindric	cylindric	ADJ
ejpam-393	965	28	algebras	algebras	PROPN
ejpam-393	965	29	mathematical	mathematical	ADJ
ejpam-393	965	30	logic	logic	NOUN
ejpam-393	965	31	quarterly	quarterly	NOUN
ejpam-393	965	32	55(6)(2009)p.666	55(6)(2009)p.666	NUM
ejpam-393	965	33	-	-	SYM
ejpam-393	965	34	668	668	NUM
ejpam-393	965	35	[	[	X
ejpam-393	965	36	40	40	NUM
ejpam-393	965	37	]	]	PUNCT
ejpam-393	965	38	t.	t.	PROPN
ejpam-393	965	39	sayed	sayed	PROPN
ejpam-393	965	40	ahmed	ahmed	PROPN
ejpam-393	965	41	.	.	PUNCT
ejpam-393	966	1	the	the	DET
ejpam-393	966	2	class	class	NOUN
ejpam-393	966	3	of	of	ADP
ejpam-393	966	4	polyadic	polyadic	PROPN
ejpam-393	966	5	algebras	algebras	PROPN
ejpam-393	966	6	has	have	VERB
ejpam-393	966	7	the	the	DET
ejpam-393	966	8	superamalgamation	superamalgamation	NOUN
ejpam-393	966	9	property	property	NOUN
ejpam-393	966	10	mathematical	mathematical	ADJ
ejpam-393	966	11	logic	logic	NOUN
ejpam-393	966	12	quarterly	quarterly	NOUN
ejpam-393	966	13	56(1)(2010)p.103	56(1)(2010)p.103	NUM
ejpam-393	966	14	-	-	SYM
ejpam-393	966	15	112	112	NUM
ejpam-393	966	16	[	[	X
ejpam-393	966	17	41	41	NUM
ejpam-393	966	18	]	]	X
ejpam-393	966	19	t.	t.	PROPN
ejpam-393	966	20	sayed	sayed	PROPN
ejpam-393	966	21	ahmed	ahme	VERB
ejpam-393	966	22	on	on	ADP
ejpam-393	966	23	neat	neat	ADJ
ejpam-393	966	24	embedding	embedding	NOUN
ejpam-393	966	25	of	of	ADP
ejpam-393	966	26	algebraisations	algebraisation	NOUN
ejpam-393	966	27	of	of	ADP
ejpam-393	966	28	first	first	ADJ
ejpam-393	966	29	order	order	NOUN
ejpam-393	966	30	logic	logic	NOUN
ejpam-393	966	31	journal	journal	NOUN
ejpam-393	966	32	of	of	ADP
ejpam-393	966	33	algebra	algebra	PROPN
ejpam-393	966	34	,	,	PUNCT
ejpam-393	966	35	number	number	NOUN
ejpam-393	966	36	theory	theory	NOUN
ejpam-393	966	37	,	,	PUNCT
ejpam-393	966	38	advances	advance	NOUN
ejpam-393	966	39	and	and	CCONJ
ejpam-393	966	40	applications	application	NOUN
ejpam-393	966	41	1(2	1(2	NUM
ejpam-393	966	42	)	)	PUNCT
ejpam-393	966	43	2009	2009	NUM
ejpam-393	967	1	p.	p.	NOUN
ejpam-393	967	2	113	113	NUM
ejpam-393	967	3	-	-	SYM
ejpam-393	967	4	125	125	NUM
ejpam-393	967	5	[	[	SYM
ejpam-393	967	6	42	42	NUM
ejpam-393	967	7	]	]	PUNCT
ejpam-393	967	8	t.	t.	PROPN
ejpam-393	967	9	sayed	sayed	PROPN
ejpam-393	967	10	ahmed	ahme	VERB
ejpam-393	967	11	the	the	DET
ejpam-393	967	12	amalgmation	amalgmation	NOUN
ejpam-393	967	13	property	property	NOUN
ejpam-393	967	14	,	,	PUNCT
ejpam-393	967	15	and	and	CCONJ
ejpam-393	967	16	a	a	DET
ejpam-393	967	17	problem	problem	NOUN
ejpam-393	967	18	of	of	ADP
ejpam-393	967	19	henkin	henkin	PROPN
ejpam-393	967	20	monk	monk	NOUN
ejpam-393	967	21	and	and	CCONJ
ejpam-393	967	22	tarski	tarski	ADJ
ejpam-393	967	23	journal	journal	NOUN
ejpam-393	967	24	of	of	ADP
ejpam-393	967	25	algebra	algebra	PROPN
ejpam-393	967	26	,	,	PUNCT
ejpam-393	967	27	number	number	NOUN
ejpam-393	967	28	theory	theory	NOUN
ejpam-393	967	29	,	,	PUNCT
ejpam-393	967	30	advances	advance	NOUN
ejpam-393	967	31	and	and	CCONJ
ejpam-393	967	32	applications	application	NOUN
ejpam-393	967	33	1(2	1(2	NUM
ejpam-393	967	34	)	)	PUNCT
ejpam-393	967	35	2009	2009	NUM
ejpam-393	968	1	p.	p.	NOUN
ejpam-393	968	2	127	127	NUM
ejpam-393	968	3	-	-	SYM
ejpam-393	968	4	141	141	NUM
ejpam-393	968	5	[	[	X
ejpam-393	968	6	43	43	NUM
ejpam-393	968	7	]	]	X
ejpam-393	968	8	t.	t.	PROPN
ejpam-393	968	9	sayed	sayed	PROPN
ejpam-393	968	10	ahmed	ahme	VERB
ejpam-393	968	11	the	the	DET
ejpam-393	968	12	class	class	NOUN
ejpam-393	968	13	of	of	ADP
ejpam-393	968	14	polyadic	polyadic	PROPN
ejpam-393	968	15	algebras	algebras	PROPN
ejpam-393	968	16	has	have	VERB
ejpam-393	968	17	the	the	DET
ejpam-393	968	18	superamalgamation	superamalgamation	NOUN
ejpam-393	968	19	property	property	NOUN
ejpam-393	968	20	mathematical	mathematical	ADJ
ejpam-393	968	21	logic	logic	NOUN
ejpam-393	968	22	quarterly	quarterly	NOUN
ejpam-393	968	23	56(1)(2010)p.103	56(1)(2010)p.103	NUM
ejpam-393	968	24	-	-	SYM
ejpam-393	968	25	112	112	NUM
ejpam-393	968	26	[	[	X
ejpam-393	968	27	44	44	NUM
ejpam-393	968	28	]	]	PUNCT
ejpam-393	968	29	t.	t.	PROPN
ejpam-393	968	30	sayed	sayed	PROPN
ejpam-393	968	31	ahmed	ahme	VERB
ejpam-393	968	32	some	some	DET
ejpam-393	968	33	results	result	NOUN
ejpam-393	968	34	on	on	ADP
ejpam-393	968	35	neat	neat	ADJ
ejpam-393	968	36	reducts	reduct	NOUN
ejpam-393	968	37	algebra	algebra	NOUN
ejpam-393	968	38	universalis	universali	VERB
ejpam-393	968	39	,	,	PUNCT
ejpam-393	968	40	in	in	ADP
ejpam-393	968	41	press	press	NOUN
ejpam-393	968	42	.	.	PUNCT
ejpam-393	969	1	references	reference	NOUN
ejpam-393	969	2	880	880	NUM
ejpam-393	969	3	[	[	SYM
ejpam-393	969	4	45	45	NUM
ejpam-393	969	5	]	]	PUNCT
ejpam-393	969	6	t.	t.	PROPN
ejpam-393	969	7	sayed	sayed	PROPN
ejpam-393	969	8	ahmed	ahmed	PROPN
ejpam-393	969	9	,	,	PUNCT
ejpam-393	969	10	i.	i.	NOUN
ejpam-393	969	11	németi	németi	PROPN
ejpam-393	969	12	,	,	PUNCT
ejpam-393	969	13	on	on	ADP
ejpam-393	969	14	neat	neat	ADJ
ejpam-393	969	15	reducts	reduct	NOUN
ejpam-393	969	16	of	of	ADP
ejpam-393	969	17	algebras	algebra	NOUN
ejpam-393	969	18	of	of	ADP
ejpam-393	969	19	logic	logic	NOUN
ejpam-393	969	20	.	.	PUNCT
ejpam-393	970	1	studia	studia	PROPN
ejpam-393	970	2	logica	logica	PROPN
ejpam-393	970	3	,	,	PUNCT
ejpam-393	970	4	62	62	NUM
ejpam-393	970	5	(	(	PUNCT
ejpam-393	970	6	2	2	NUM
ejpam-393	970	7	)	)	PUNCT
ejpam-393	970	8	(	(	PUNCT
ejpam-393	970	9	2001	2001	NUM
ejpam-393	970	10	)	)	PUNCT
ejpam-393	970	11	,	,	PUNCT
ejpam-393	970	12	p.229	p.229	PROPN
ejpam-393	970	13	-	-	PUNCT
ejpam-393	970	14	262	262	NUM
ejpam-393	970	15	.	.	PUNCT
ejpam-393	971	1	[	[	X
ejpam-393	971	2	46	46	NUM
ejpam-393	971	3	]	]	PUNCT
ejpam-393	971	4	t.sayed	t.saye	VERB
ejpam-393	971	5	ahmed	ahmed	PROPN
ejpam-393	971	6	and	and	CCONJ
ejpam-393	971	7	m.	m.	NOUN
ejpam-393	971	8	amer	amer	PROPN
ejpam-393	971	9	polyadic	polyadic	PROPN
ejpam-393	971	10	and	and	CCONJ
ejpam-393	971	11	cylindric	cylindric	ADJ
ejpam-393	971	12	algebras	algebra	NOUN
ejpam-393	971	13	of	of	ADP
ejpam-393	971	14	sentences	sentence	NOUN
ejpam-393	971	15	mathematical	mathematical	ADJ
ejpam-393	971	16	logic	logic	NOUN
ejpam-393	971	17	quaterly	quaterly	ADV
ejpam-393	971	18	vol	vol	VERB
ejpam-393	971	19	52	52	NUM
ejpam-393	971	20	no	no	DET
ejpam-393	971	21	5	5	NUM
ejpam-393	971	22	p.44	p.44	NOUN
ejpam-393	971	23	-	-	X
ejpam-393	971	24	49	49	NUM
ejpam-393	971	25	(	(	PUNCT
ejpam-393	971	26	2006	2006	NUM
ejpam-393	971	27	)	)	PUNCT
ejpam-393	972	1	[	[	X
ejpam-393	972	2	47	47	NUM
ejpam-393	972	3	]	]	PUNCT
ejpam-393	972	4	t.	t.	PROPN
ejpam-393	972	5	sayed	sayed	PROPN
ejpam-393	972	6	ahmed	ahmed	PROPN
ejpam-393	972	7	and	and	CCONJ
ejpam-393	972	8	b.samir	b.samir	X
ejpam-393	972	9	a	a	DET
ejpam-393	972	10	neat	neat	ADJ
ejpam-393	972	11	embedding	embed	VERB
ejpam-393	972	12	theorem	theorem	NOUN
ejpam-393	972	13	for	for	ADP
ejpam-393	972	14	expansions	expansion	NOUN
ejpam-393	972	15	of	of	ADP
ejpam-393	972	16	cylindric	cylindric	ADJ
ejpam-393	972	17	algebras	algebras	PROPN
ejpam-393	972	18	logic	logic	PROPN
ejpam-393	972	19	journal	journal	PROPN
ejpam-393	972	20	of	of	ADP
ejpam-393	972	21	igpl	igpl	ADJ
ejpam-393	972	22	15	15	NUM
ejpam-393	972	23	(	(	PUNCT
ejpam-393	972	24	2007	2007	NUM
ejpam-393	972	25	)	)	PUNCT
ejpam-393	973	1	p.	p.	NOUN
ejpam-393	973	2	41	41	NUM
ejpam-393	974	1	-	-	SYM
ejpam-393	974	2	51	51	NUM
ejpam-393	975	1	[	[	X
ejpam-393	975	2	48	48	NUM
ejpam-393	975	3	]	]	PUNCT
ejpam-393	975	4	i.	i.	PROPN
ejpam-393	975	5	sain	sain	PROPN
ejpam-393	975	6	.	.	PUNCT
ejpam-393	976	1	searching	search	VERB
ejpam-393	976	2	for	for	ADP
ejpam-393	976	3	a	a	DET
ejpam-393	976	4	finitizable	finitizable	ADJ
ejpam-393	976	5	algebraization	algebraization	NOUN
ejpam-393	976	6	of	of	ADP
ejpam-393	976	7	first	first	ADJ
ejpam-393	976	8	order	order	NOUN
ejpam-393	976	9	logic	logic	NOUN
ejpam-393	976	10	.	.	PUNCT
ejpam-393	977	1	logic	logic	ADJ
ejpam-393	977	2	journal	journal	PROPN
ejpam-393	977	3	of	of	ADP
ejpam-393	977	4	igpl	igpl	ADJ
ejpam-393	977	5	.	.	PUNCT
ejpam-393	978	1	oxford	oxford	PROPN
ejpam-393	978	2	university	university	PROPN
ejpam-393	978	3	press	press	NOUN
ejpam-393	978	4	.	.	PUNCT
ejpam-393	979	1	8(4	8(4	X
ejpam-393	979	2	)	)	PUNCT
ejpam-393	979	3	(	(	PUNCT
ejpam-393	979	4	2000	2000	NUM
ejpam-393	979	5	)	)	PUNCT
ejpam-393	979	6	,	,	PUNCT
ejpam-393	980	1	495–589	495–589	NUM
ejpam-393	980	2	.	.	PUNCT
ejpam-393	981	1	[	[	X
ejpam-393	981	2	49	49	NUM
ejpam-393	981	3	]	]	X
ejpam-393	981	4	g.	g.	PROPN
ejpam-393	981	5	sagi	sagi	PROPN
ejpam-393	981	6	,	,	PUNCT
ejpam-393	981	7	a	a	DET
ejpam-393	981	8	completeness	completeness	NOUN
ejpam-393	981	9	theorem	theorem	VERB
ejpam-393	981	10	for	for	ADP
ejpam-393	981	11	higher	high	ADJ
ejpam-393	981	12	order	order	NOUN
ejpam-393	981	13	logics	logic	NOUN
ejpam-393	981	14	journal	journal	NOUN
ejpam-393	981	15	of	of	ADP
ejpam-393	981	16	symbolic	symbolic	ADJ
ejpam-393	981	17	logic	logic	NOUN
ejpam-393	981	18	65(3)(2000	65(3)(2000	NUM
ejpam-393	981	19	)	)	PUNCT
ejpam-393	981	20	p.857	p.857	NOUN
ejpam-393	981	21	-	-	NUM
ejpam-393	981	22	884	884	NUM
ejpam-393	981	23	.	.	PUNCT
ejpam-393	982	1	[	[	X
ejpam-393	982	2	50	50	NUM
ejpam-393	982	3	]	]	PUNCT
ejpam-393	982	4	s.	s.	PROPN
ejpam-393	982	5	shelah	shelah	PROPN
ejpam-393	982	6	.	.	PUNCT
ejpam-393	983	1	classification	classification	NOUN
ejpam-393	983	2	theory	theory	NOUN
ejpam-393	983	3	second	second	PROPN
ejpam-393	983	4	edition	edition	PROPN
ejpam-393	983	5	north	north	PROPN
ejpam-393	983	6	holland	holland	PROPN
ejpam-393	983	7	p.c	p.c	PROPN
ejpam-393	983	8	.	.	PROPN
ejpam-393	983	9	,	,	PUNCT
ejpam-393	983	10	amsterdam	amsterdam	PROPN
ejpam-393	983	11	1990	1990	NUM
ejpam-393	983	12	.	.	PUNCT
ejpam-393	984	1	[	[	X
ejpam-393	984	2	51	51	NUM
ejpam-393	984	3	]	]	PUNCT
ejpam-393	984	4	a.	a.	NOUN
ejpam-393	984	5	tarski	tarski	NOUN
ejpam-393	984	6	and	and	CCONJ
ejpam-393	984	7	s.	s.	PROPN
ejpam-393	984	8	givant	givant	VERB
ejpam-393	984	9	a	a	DET
ejpam-393	984	10	formalization	formalization	NOUN
ejpam-393	984	11	of	of	ADP
ejpam-393	984	12	set	set	NOUN
ejpam-393	984	13	theory	theory	NOUN
ejpam-393	984	14	without	without	ADP
ejpam-393	984	15	variables	variable	NOUN
ejpam-393	984	16	.	.	PUNCT
ejpam-393	985	1	ams	am	NOUN
ejpam-393	985	2	colloquium	colloquium	NOUN
ejpam-393	985	3	publications	publication	NOUN
ejpam-393	985	4	41	41	NUM
ejpam-393	985	5	,	,	PUNCT
ejpam-393	985	6	(	(	PUNCT
ejpam-393	985	7	1987	1987	NUM
ejpam-393	985	8	)	)	PUNCT
ejpam-393	985	9	.	.	PUNCT