Winning the pressing down game but not Banach Mazur
classification
🧮 math.LO
keywords
omegagamebanachdownlengthmazurpressingalpha
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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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