Ultrafilters and independent sets

Kunen, Kenneth

doi:10.1090/S0002-9947-1972-0314619-7

Ultrafilters and independent sets
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Trans. Amer. Math. Soc. 172 (1972), 299-306 Request permission

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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