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Winning the pressing down game but not Banach Mazur

Jakob Kellner·Matti Pauna·Saharon Shelah
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Abstract

Let $S$ be the set of those $α\inω_2$ that have cofinality $ω_1$. It is consistent relative to a measurable that the nonempty player wins the pressing down game of length $ω_1$, but not the Banach Mazur game of length $ω+1$ (both games starting with $S$).

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Jakob Kellner, Matti Pauna, Saharon Shelah. 2007-02-17. Winning the pressing down game but not Banach Mazur. https://doi.org/10.2178/jsl/1203350789

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