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Finite and countable families of algebras of sets

2010
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Mathematical Research Letters
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Let {A λ } λ∈Λ be a family of algebras of sets defined on a set X, 0 < #(Λ) ≤ ℵ 0 , and A λ = P(X) for each λ ∈ Λ. We assume that A λ are σ-algebras if #(Λ) = ℵ 0 . We obtained the necessary and sufficient conditions for which λ∈Λ A λ = P(X). In the formulation of these conditions we use ω-saturated algebras and finite sequences of ultrafilters on X. 1. The formulation of results 1.1. The object of our present investigation is algebras of sets. The present article is a further development of

doi:10.4310/mrl.2010.v17.n4.a3
fatcat:spues2soirc7piyopxegy6xn7y