Determinacy and indeterminacy of games played on complete metric spaces

Authors

  • L. Fishman University of North Texas,
  • T. Ly Brandeis University,
  • D. Simmons Ohio State University

Keywords:

Gale-Stewart games, game determinacy, Schmidt games,

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 (for example fractals). We show that except for certain exceptional cases, these games are undetermined on certain sets. Judging by the vast numbers of papers utilising these games, we believe that the results in this paper will be of interest to a large audience of number theorists as well as set theorists and logicians. DOI: 10.1017/S0004972714000069

Author Biography

D. Simmons, Ohio State University

Department of Mathematics Zassenhaus Assistant Professor

Published

2014-08-03

Issue

Vol. 90 No. 2 (2014)

Section

Articles
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