Mathias forcing and combinatorial covering properties of filters

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Journal of Symbolic Logic 80 (4):1398-1410 (2015)
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Abstract

We give topological characterizations of filters${\cal F}$onωsuch that the Mathias forcing${M_{\cal F}}$adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzmán, Hrušák, Martínez, Minami, and Tsaban.

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10.1017/jsl.2014.73

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Covering properties of $$omega $$ω -mad families.Leandro Aurichi & Lyubomyr Zdomskyy - 2020 - Archive for Mathematical Logic 59 (3-4):445-452.

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References found in this work

Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Mathias–Prikry and Laver–Prikry type forcing.Michael Hrušák & Hiroaki Minami - 2014 - Annals of Pure and Applied Logic 165 (3):880-894.
Near coherence of filters. I. Cofinal equivalence of models of arithmetic.Andreas Blass - 1986 - Notre Dame Journal of Formal Logic 27 (4):579-591.
Forcing with filters and complete combinatorics.Claude Laflamme - 1989 - Annals of Pure and Applied Logic 42 (2):125-163.
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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