On sets not belonging to algebras

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

3 اقتباسات (Scopus)

ملخص

Let script A sign1, . . ., script A signn script A signn+1 be a finite sequence of algebras of sets given on a set X, ∪nk=1 script A signk ≠ B-frakfur sign (X), with more than 4/3n pairwise disjoint sets not belonging to script A signn+1. It was shown in [4] and [5] that in this case ∪k-1n+1 script A signk ≠ B-frakfur sign(X). Let us consider, instead script A signn+1, a finite sequence of algebras script A signn+1, . . . , script A signn+l. It turns out that if for each natural i ≤ l there exist no less than 4/3(n + l) - l/24 pairwise disjoint sets not belonging to script A signn+i, then ∪k=1n+1 script A signk ≠ B-frakfur sign(X). But if l ≥ 195 and if for each natural i ≤ l there exist no less than 4/3(n + l) - l/15 pairwise disjoint sets not belonging to script A signn+i, then ∪k=1n+lscript A sign k ≠ B-frakfur sign(X). After consideration of finite sequences of algebras, it is natural to consider countable sequences of algebras. We obtained two essentially important theorems on a countable sequence of almost σ-algebras (the concept of almost σ -algebra was introduced in [4]).

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)483-500
عدد الصفحات18
دوريةJournal of Symbolic Logic
مستوى الصوت72
رقم الإصدار2
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - يونيو 2007

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