Mathias forcing and combinatorial covering properties of filters

David Chodounsk\'y; Du\v{s}an Repov\v{s}; Lyubomyr Zdomskyy

arxiv: 1401.2283 · v2 · pith:47YUFRL3new · submitted 2014-01-10 · 🧮 math.LO · math.GN

Mathias forcing and combinatorial covering properties of filters

David Chodounsk\'y , Du\v{s}an Repov\v{s} , Lyubomyr Zdomskyy This is my paper

classification 🧮 math.LO math.GN

keywords filtersforcingmathiasaddsallowsanswerbrendlecharacterizations

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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, Guzm\'an, Hru\v{s}\'ak, Mart\'{\i}nez, Minami, and Tsaban.

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Mathias forcing and combinatorial covering properties of filters

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