Strong measure zero and infinite games

Archive for Mathematical Logic 56 (7-8):725-732 (2017)

Abstract

We show that strong measure zero sets -totally bounded metric space) can be characterized by the nonexistence of a winning strategy in a certain infinite game. We use this characterization to give a proof of the well known fact, originally conjectured by K. Prikry, that every dense \ subset of the real line contains a translate of every strong measure zero set. We also derive a related result which answers a question of J. Fickett.

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Robert Solovay
University of California, Berkeley

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