Finite and countable families of algebras of sets

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Let {Aλ} λ ε ∧ be a family of algebras of sets defined on a set X, 0 < ≠(∧) ≥ א0, and Aλ ≠ P(X) for each λ ε ∧. We assume that Aλ are σ-algebras if ≠( ∧) = א0. We obtained the necessary and sufficient conditions for which ∪λ ε ∧ Aλ = P(X). In the formulation of these conditions we use ω-saturated algebras and finite sequences of ultrafilters on X.

Original languageEnglish
Pages (from-to)613-623
Number of pages11
JournalMathematical Research Letters
Issue number4
StatePublished - Jul 2010


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