Ultrafilters and independent sets

Kunen, Kenneth

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

Ultrafilters and independent sets
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by Kenneth Kunen

Trans. Amer. Math. Soc. 172 (1972), 299-306

DOI: https://doi.org/10.1090/S0002-9947-1972-0314619-7

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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.

References

Model theory

R. Engelking and M. Karłowicz, Some theorems of set theory and their topological consequences, Fund. Math. 57 (1965), 275–285. MR 196693, DOI 10.4064/fm-57-3-275-285

Sur les opérations linéairs dans l’espace des fonctions bornées

5

Über zwei Sätze von G. Fichtenholz und L. Kantorovitch

6

Kenneth Kunen, Some applications of iterated ultrapowers in set theory, Ann. Math. Logic 1 (1970), 179–227. MR 277346, DOI 10.1016/0003-4843(70)90013-6
K. Kunen and J. B. Paris, Boolean extensions and measurable cardinals, Ann. Math. Logic 2 (1970/71), no. 4, 359–377. MR 277381, DOI 10.1016/0003-4843(71)90001-5
Mary Ellen Rudin, Partial orders on the types in $\beta N$, Trans. Amer. Math. Soc. 155 (1971), 353–362. MR 273581, DOI 10.1090/S0002-9947-1971-0273581-5
Saharon Shelah, Every two elementarily equivalent models have isomorphic ultrapowers, Israel J. Math. 10 (1971), 224–233. MR 297554, DOI 10.1007/BF02771574