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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Mad families and ultrafilters

Author: Martin Weese
Journal: Proc. Amer. Math. Soc. 80 (1980), 475-477
MSC: Primary 54A25; Secondary 03E35, 04A20
MathSciNet review: 581008
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Abstract: For each almost disjoint family X let $ F(X) = \{ a \subseteq \omega :{\text{card}}\{ s \in X:s\backslash a\;{\text{is... ...\text{card}}\;\{ s \in X:{\text{card}}\;(s \cap a) = \omega \} = {2^\omega }\} $ . Assuming $ P({2^\omega })$ we show that for each nonprincipal ultrafilter p there exist a maximal almost disjoint family X and an almost disjoint family Y with $ F(X) = I(Y) = p$.

References [Enhancements On Off] (What's this?)

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Keywords: Almost disjoint family, Stone-Čech compactification, $ {2^\omega }$-point, superatomic Boolean algebra
Article copyright: © Copyright 1980 American Mathematical Society

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