id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2814	Abbas, Hind; Ebrahim, hassan; Al-Fayadh, Ali	Some Properties for the Restriction of P^*-field of Sets	2022	6	.pdf	application/pdf	2110	149	86	The proof is done by proposition 2.6 and 3.2 Theorem 3.10 Assume ℐ ⊆ P(𝒰) and Φ ≠ ℬ ⊆ 𝒰, then 𝒫∗ (ℐ|ℬ) is the smallest 𝒫∗– field on ℬ that contain ℐ|ℬ , where 𝒫∗ (ℐ|ℬ) = ⋂{ℳi|ℬ: ℳi|ℬ is a 𝒫∗– field of ℬ and ℳi|ℬ ⊇ ℐ|ℬ, ∀i ∈ Ι}. Therefore, 𝒫(ℐ|ℬ) is the smallest 𝒫∗– field on ℬ containing ℐ|ℬ. Theorem 3.11 If ℐ ⊆ P(𝒰) and Φ ≠ ℬ ⊆ 𝒰, define a class ℳ by: ℳ ={M ⊆ 𝒰 : M⋂ ℬ ϵ 𝒫∗(ℐ|ℬ) }.	cache/iajs-2814.pdf	txt/iajs-2814.txt