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Mathias forcing and combinatorial covering properties of filters
Chodounský, David ; Repovš, Dušan, 1954- ; Zdomskyy, Lyubomyr, 1983-
We give topological characterizations of filters ▫$\mathcal{F}$▫ on ▫$w$▫ such that the Mathias forcing ▫$M_\mathcal{F}$▫ 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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