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 -