Mathias forcing and combinatorial covering properties of filters

2014/01/31 by David Chodounský, Dušan Repovš, Lyubomyr Zdomskyy · 1 citation
Mathematics · #math.LO #math.GN #msc:54D20 #msc:03E40 #msc:54H05 #msc:03E05

paper · pdf · doi:10.1017/jsl.2014.73

published as Journal of Symbolic Logic, volume 80, issue 04, 2015, pp. 1398-1410 · 12 pages, comments are welcome

arxiv created 2015/04/08 · arxiv updated 2015/12/29

Abstract

We give topological characterizations of filters F on w such that the Mathias forcing M_F adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzmán, Hrušák, Mart'ınez, Minami, and Tsaban.

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• Combinatorial covering properties in an uncountable setting: canonical examples

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