On the cofinality of ultrapowers

1996/11/29 by Andreas Blass, Blass, Andreas, Heike Mildenberger +1 · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/9611210

openalex publication_date 1996/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

All ultrafilters under consideration here are non-principal ultrafilters on the set omega of natural numbers. We are concerned with the possible cofinalities of ultrapowers of omega with respect to such ultrafilters. We show that no cardinal below the groupwise density number g can occur as such a cofinality and that at most one cardinal below the splitting number s can so occur. The proof for s, when combined with a result of Nyikos, gives the additional information that all P_kappa-point ultrafilters, for kappa greater than the bounding number b, are nearly coherent.

Cited by

• On a variation of selective separability using ideals

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• On Ultrapowers and Cohesive Ultrafilters
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