Limitations on representing P(X) as a union of proper subalgebras

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For every integer μ ≥ 3, there exists a function fμ: N+ → N+ such that the following holds: (1) fμ(k) = 2k − μ for k large enough; (2) if A is a finite nonempty collection of subalgebras of P(X) such that ⊓ B is not fμ (#(B))-saturated, for all nonempty B ⊆ A, then ⊔ A ≠ P(X).

Original languageEnglish
Pages (from-to)859-868
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - 2015


  • Algebras of sets
  • Ultrafilter
  • σ-algebra


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