DETERMINACY AND INDETERMINACY OF GAMES PLAYED ON COMPLETE METRIC SPACES

作者：Fishman Lior; Ly Tue; Simmons David^*

来源：Bulletin of the Australian Mathematical Society, 2014, 90(2): 339-351.

DOI：10.1017/S0004972714000069

• determinacy of games
• Borel determinacy
• Gale-Stewart games
• Schmidt%26apos
• s game

Schmidt%26apos;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%26apos;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.

• 出版日期2014-10