Abstract
We investigate the pressing down game and its relation to the Banach Mazur game. In particular we show: consistently, there is a nowhere precipitous normal ideal I on \({\aleph_2}\) such that player nonempty wins the pressing down game of length \({\aleph_1}\) on I even if player empty starts.
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Kellner, J., Shelah, S. More on the pressing down game. Arch. Math. Logic 50, 477–501 (2011). https://doi.org/10.1007/s00153-011-0227-x
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DOI: https://doi.org/10.1007/s00153-011-0227-x