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Winning the pressing down game but not Banach-Mazur

Published online by Cambridge University Press:  12 March 2014

Jakob Kellner ,
Matti Pauna  and
Saharon Shelah
Jakob Kellner
Affiliation:
Kurt Gödel Research Center for Mathematical Logic, Universität Wien, Wahringer Straße 25, 1090 Wien, Austria. E-mail: kellner@fsmat.at, URL: http://www.logic.univie.ac.at/~kellner Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904., Israel
Matti Pauna
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin Katu 2B, Fin-00014, Finland. E-mail: matti.pauna@helsinki.fi, URL: http://www.helsinki.fi/~pauna/ Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904., Israel
Saharon Shelah
Affiliation:
Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904., Israel Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA. E-mail: shelah@math.huji.ac.il, URL: http://shelah.logic.at/
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Abstract

Let S be the set of those α ∈ ω2 that have cofinality ω1. It is consistent relative to a measurable that the nonempty player wins the pressing down game of length ω1, but not the Banach-Mazur game of length ω + 1 (both games starting with S).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 4 , December 2007 , pp. 1323 - 1335
Copyright
Copyright © Association for Symbolic Logic 2007

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