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Covering the Baire space by families which are not finitely dominating
Annals of Pure and Applied Logic 140 (1):60-71 (2006)
Abstract
It is consistent that each union of many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter , the cofinality of the reduced ultrapower is greater than . The model is constructed by oracle chain condition forcing, to which we give a self-contained introductionLinks
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Citations of this work
Combinatorial images of sets of reals and semifilter trichotomy.Boaz Tsaban & Lyubomyr Zdomskyy - 2008 - Journal of Symbolic Logic 73 (4):1278-1288.
Selective covering properties of product spaces.Arnold W. Miller, Boaz Tsaban & Lyubomyr Zdomskyy - 2014 - Annals of Pure and Applied Logic 165 (5):1034-1057.
Exactly two and exactly three near-coherence classes.Heike Mildenberger - 2023 - Journal of Mathematical Logic 24 (1).
The minimal cofinality of an ultrapower of ω and the cofinality of the symmetric group can be larger than b+.Heike Mildenberger & Saharon Shelah - 2011 - Journal of Symbolic Logic 76 (4):1322-1340.
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.
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.
Maximal chains inωω and ultrapowers of the integers.Saharon Shelah & Juris Steprāns - 1993 - Archive for Mathematical Logic 32 (5):305-319.
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