A GAME‐THEORETIC PROOF OF ANALYTIC RAMSEY THEOREM

Kazuyuki Tanaka

doi:10.1002/malq.19920380127

A GAME‐THEORETIC PROOF OF ANALYTIC RAMSEY THEOREM

Kazuyuki Tanaka

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 language	English
Pages (from-to)	301-304
Number of pages	4
Journal	Mathematical Logic Quarterly
Volume	38
Issue number	1
DOIs	https://doi.org/10.1002/malq.19920380127
Publication status	Published - 1992

Keywords

Analytic Ramsey theorem
determinacy of infinite games

ASJC Scopus subject areas

Logic

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