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Winning strategies in club games and their applications
Author(s) -
König Bernhard
Publication year - 2011
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200910119
Subject(s) - club , mathematics , mathematical economics , mathematics education , geology , paleontology
We present results concerning winning strategies and tactics in club games on ω 1λ . We show that there is generally no winning tactic for the player trying to get inside the club. The bound‐countable game turns out to be rather fruitful and adds to some previous results about the construction of elementary substructures and their localization in certain intervals. We show that Player II has a winning strategy in the bound‐countable game, thus establishing a new ZFC result. The applications given are new proofs for two cardinal diamonds and the impossibility of collapsing cardinals to ℵ 2 under certain conditions (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)