✦ LIBER ✦

A GAME-THEORETIC PROOF OF ANALYTIC RAMSEY THEOREM

✍ Scribed by Kazuyuki Tanaka

Publisher: John Wiley and Sons
Year: 1992
Tongue: English
Weight: 217 KB
Volume: 38
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19920380127

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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