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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Ultrafilters and independent sets


Author: Kenneth Kunen
Journal: Trans. Amer. Math. Soc. 172 (1972), 299-306
MSC: Primary 02J05; Secondary 02H13
MathSciNet review: 0314619
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Abstract: Independent families of sets and of functions are used to prove some theorems about ultrafilters. All of our results are well known to be provable from some form of the generalized continuum hypothesis, but had remained open without such an assumption. Independent sets are used to show that the Rudin-Keisler ordering on ultrafilters is nonlinear. Independent functions are used to prove the existence of good ultrafilters.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0314619-7
Keywords: Ultrafilter, independent sets, Rudin-Keisler ordering, independent functions, good ultrafilter
Article copyright: © Copyright 1972 American Mathematical Society