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- W1585604493 abstract "We introduce a property of posets which strengthens (omega_1+1)-strategic closedness. This property is defined using a variation of the Banach-Mazur game on posets, where the first player chooses a countable set of conditions instead of a single condition at each turn. We prove PFA is preserved under any forcing over a poset with this property. As an application we reproduce a proof of Magidor's theorem about the consistency of PFA with some weak variations of the square principles. We also argue how different this property is from (omega_1+1)-operational closedness, which we introduced in our previous work, by observing which portions of MA^+(omega_1-closed) are preserved or destroyed under forcing over posets with either property." @default.
- W1585604493 created "2016-06-24" @default.
- W1585604493 creator A5057269032 @default.
- W1585604493 date "2015-03-23" @default.
- W1585604493 modified "2023-09-27" @default.
- W1585604493 title "The *-variation of the Banach-Mazur game and forcing axioms" @default.
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- W1585604493 hasPublicationYear "2015" @default.
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