Winning the pressing down game but not Banach Mazur

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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 $S$).
New version: some improvements in presentation, references, history; main theorem slightly strengthened; some typos removed

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Logic, 03E35;03E55

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http://salesiana.dossiersoluciones.com/handle/123456789/157618

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0609655
 http://arxiv.org/abs/math/0609655
 J. Symbolic Logic 72 (2007), No. 4, 1323--1335
 doi:10.2178/jsl/1203350789

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arXiv