On the cofinality of ultrapowers

Journal of Symbolic Logic 64 (2):727-736 (1999)
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Abstract

We prove some restrictions on the possible cofinalities of ultrapowers of the natural numbers with respect to ultrafilters on the natural numbers. The restrictions involve three cardinal characteristics of the continuum, the splitting number s, the unsplitting number r, and the groupwise density number g. We also prove some related results for reduced powers with respect to filters other than ultrafilters

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References found in this work

Special ultrafilters and cofinal subsets of $$({}^omega omega, <^*)$$.Peter Nyikos - 2020 - Archive for Mathematical Logic 59 (7-8):1009-1026.
Near coherence of filters. I. Cofinal equivalence of models of arithmetic.Andreas Blass - 1986 - Notre Dame Journal of Formal Logic 27 (4):579-591.
Countable ultraproducts without CH.Michael Canjar - 1988 - Annals of Pure and Applied Logic 37 (1):1-79.
Cofinalities of countable ultraproducts: the existence theorem.R. Michael Canjar - 1989 - Notre Dame Journal of Formal Logic 30 (4):539-542.

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