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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Almost disjoint refinement of families of subsets of $ {\bf N}$


Authors: Bohuslav Balcar and Peter Vojtáš
Journal: Proc. Amer. Math. Soc. 79 (1980), 465-470
MSC: Primary 04A20; Secondary 54A25, 54D40
MathSciNet review: 567994
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Abstract: Without any set-theoretic assumptions, we prove that every uniform ultrafilter on the set N of all natural numbers has a Comfort system, that is, an almost disjoint refinement. Moreover, we describe one type of ideal such that the family of all subsets of N that are not contained in it has an almost disjoint refinement.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0567994-2
PII: S 0002-9939(1980)0567994-2
Keywords: Ultrafilter, almost disjoint family, $ {2^\omega }$-point, refinement
Article copyright: © Copyright 1980 American Mathematical Society