On the cofinality of ultrapowers
Journal of Symbolic Logic 64 (2):727-736 (1999)
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 ultrafiltersDOI
10.2307/2586495
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Citations of this work
Special ultrafilters and cofinal subsets of $$({}^omega omega, <^*)$$.Peter Nyikos - 2020 - Archive for Mathematical Logic 59 (7-8):1009-1026.
Selective covering properties of product spaces.Arnold W. Miller, Boaz Tsaban & Lyubomyr Zdomskyy - 2014 - Annals of Pure and Applied Logic 165 (5):1034-1057.
On the length of chains of proper subgroups covering a topological group.Taras Banakh, Dušan Repovš & Lyubomyr Zdomskyy - 2011 - Archive for Mathematical Logic 50 (3-4):411-421.
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References found in this work
There may be simple Pℵ1 and Pℵ2-points and the Rudin-Keisler ordering may be downward directed.Andreas Blass & Saharon Shelah - 1987 - Annals of Pure and Applied Logic 33 (C):213-243.
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.
