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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