Winning the pressing down game but not Banach Mazur

Jakob Kellner; Matti Pauna; Saharon Shelah

doi:10.2178/jsl/1203350789

Winning the pressing down game but not Banach Mazur

Logic 2008-03-30 v2

Authors: Jakob Kellner , Matti Pauna , Saharon Shelah

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Abstract

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 $S$ ).

Keywords

pressing down game banach mazur game consistency measurable cardinal set theory

Cite

@article{arxiv.math/0609655,
  title  = {Winning the pressing down game but not Banach Mazur},
  author = {Jakob Kellner and Matti Pauna and Saharon Shelah},
  journal= {arXiv preprint arXiv:math/0609655},
  year   = {2008}
}

Comments

New version: some improvements in presentation, references, history; main theorem slightly strengthened; some typos removed

Winning the pressing down game but not Banach Mazur

Abstract

Keywords

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