Strong measure zero and infinite games

We show that strong measure zero sets (in a σ -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 G δ subse...

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Bibliographic Details
Published in:Archive for mathematical logic 2017-11, Vol.56 (7-8), p.725-732
Main Authors: Galvin, Fred, Mycielski, Jan, Solovay, Robert M.
Format: Article
Language:English
Subjects:
Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
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Summary:We show that strong measure zero sets (in a σ -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 G δ 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.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-017-0541-z