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

L. Grinblat

doi:10.1090/S0002-9939-2014-12220-9

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

L. Grinblat

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

For every integer μ ≥ 3, there exists a function f_μ: N₊ → N₊ such that the following holds: (1) f_μ(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 f_μ (#(B))-saturated, for all nonempty B ⊆ A, then ⊔ A ≠ P(X).

Original language	English
Pages (from-to)	859-868
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-2014-12220-9
State	Published - 2015

Keywords

Algebras of sets
Ultrafilter
σ-algebra

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10.1090/S0002-9939-2014-12220-9

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abstract = "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).",

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KW - σ-algebra

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

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Keywords

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