TY - JOUR

T1 - Limitations on representing P(X) as a union of proper subalgebras

AU - Grinblat, L.

N1 - Publisher Copyright:
© 2014 American Mathematical Society.

PY - 2015

Y1 - 2015

N2 - 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).

AB - 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).

KW - Algebras of sets

KW - Ultrafilter

KW - σ-algebra

UR - http://www.scopus.com/inward/record.url?scp=84919338031&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2014-12220-9

DO - 10.1090/S0002-9939-2014-12220-9

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AN - SCOPUS:84919338031

SN - 0002-9939

VL - 143

SP - 859

EP - 868

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -