Winning the pressing down game but not Banach Mazur

Details Winning the pressing down game but not Banach Mazur Winning the pressing down game but not Banach Mazur

2006-09-25

arxiv.org/abs/math/0609655v2

J. Symbolic Logic 72 (2007), No. 4, 1323--1335

Mathematics

Logic

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

Scientific paper

10.2178/jsl/1203350789

Let $S$ be the set of those $\alpha\in\omega_2$ that have cofinality
$\omega_1$. It is consistent relative to a measurable that the nonempty player
wins the pressing down game of length $\omega_1$, but not the Banach Mazur game
of length $\omega+1$ (both games starting with $S$).

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