A GAME‐THEORETIC PROOF OF ANALYTIC RAMSEY THEOREM

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Abstract

We give a simple game‐theoretic proof of Silver's theorem that every analytic set is Ramsey. A set P of subsets of ω is called Ramsey if there exists an infinite set H such that either all infinite subsets of H are in P or all out of P. Our proof clarifies a strong connection between the Ramsey property of partitions and the determinacy of infinite games.

Original languageEnglish
Pages (from-to)301-304
Number of pages4
JournalMathematical Logic Quarterly
Volume38
Issue number1
DOIs
Publication statusPublished - 1992

Keywords

  • Analytic Ramsey theorem
  • determinacy of infinite games

ASJC Scopus subject areas

  • Logic

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