Determinacy and indeterminacy of games played on complete metric spaces
Logic
2019-02-20 v1
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.
Keywords
Cite
@article{arxiv.1307.3951,
title = {Determinacy and indeterminacy of games played on complete metric spaces},
author = {Lior Fishman and Tue Ly and David S. Simmons},
journal= {arXiv preprint arXiv:1307.3951},
year = {2019}
}