1 results
On sets not belonging to algebras
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- Journal:
- The Journal of Symbolic Logic / Volume 72 / Issue 2 / June 2007
- Published online by Cambridge University Press:
- 12 March 2014, pp. 483-500
- Print publication:
- June 2007
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- Article
- Export citation
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Let
be a finite sequence of algebras of sets given on a set 
with more than 
pairwise disjoint sets not belonging to 
It was shown in [4] and [5] that in this case 
Let us consider, instead 
a finite sequence of algebras 
It turns out that if for each natural i ≤ l there exist no less than 
pairwise disjoint sets not belonging to 
then 
But if l ≥ 195 and if for each natural i ≤ l there exist no less than 
pairwise disjoint sets not belonging to 
then 
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]).
be a finite sequence of algebras of sets given on a set 
with more than 
pairwise disjoint sets not belonging to 
It was shown in [4] and [5] that in this case 
Let us consider, instead 
a finite sequence of algebras 
It turns out that if for each natural 
pairwise disjoint sets not belonging to 
then 
But if 
pairwise disjoint sets not belonging to 
then 
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]).