Determinacy and indeterminacy of games played on complete metric spaces

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JournalBulletin of the Australian Mathematical Society
DatePublished - Oct 2014
Issue number2
Volume90
Number of pages13
Pages (from-to)339-351
Original languageEnglish

Abstract

Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results have been proven using this game. In this paper we address determinacy and indeterminacy questions regarding Schmidt's game and its variations, as well as more general games played on complete metric spaces (e.g. fractals). We show that except for certain exceptional cases, these games are undetermined on Bernstein sets.

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© 2014 Australian Mathematical Publishing Association Inc. This is an author produced version of a paper accepted for publication in Bulletin of the Australian Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy.

    Research areas

  • math.LO

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