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Games and ramsey-like cardinals

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)408-437
Number of pages30
JournalJournal of Symbolic Logic
Volume84
Issue number1
DOIs
DateAccepted/In press - 29 Oct 2018
DatePublished (current) - 1 Mar 2019

Abstract

We generalise the α-Ramsey cardinals introduced in Holy and Schlicht (2018) for cardinals α to arbitrary ordinals α, and answer several questions posed in that paper. In particular, we show that α-Ramseys are downwards absolute to the core model K for all α of uncountable cofinality, that strategic ω-Ramsey cardinals are equiconsistent with remarkable cardinals and that strategic α-Ramsey cardinals are equiconsistent with measurable cardinals for all α > ω. We also show that the n-Ramseys satisfy indescribability properties and use them to provide a game-theoretic characterisation of completely ineffable cardinals, as well as establishing further connections between the α-Ramsey cardinals and the Ramsey-like cardinals introduced in Gitman (2011), Feng (1990), and Sharpe and Welch (2011).

    Research areas

  • completely ineffable cardinals, core model, games, ineffable cardinals, large cardinals, measurable cardinals, Ramsey-like cardinals, remarkable cardinals, virtually measurable cardinals, weakly compact cardinals

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    Rights statement: This is the final published version of the article (version of record). It first appeared online via Cambridge University Press at https://doi.org/10.1017/jsl.2018.75 . Please refer to any applicable terms of use of the publisher.

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