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

by Kellner and Pauna and Shelah. [KPSh:896]

J Symbolic Logic, 2007

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

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