Determinacy separations for class games
Logic
2016-07-20 v1
Abstract
We show, assuming weak large cardinals, that in the context of games played in a proper class of moves, clopen determinacy is strictly weaker than open determinacy. The proof amounts to an analysis of a certain level of that exists under large cardinal assumptions weaker than an inaccessible. Our argument is sufficiently general to give a family of determinacy separation results applying in any setting where the universal class is sufficiently closed; e.g., in third, seventh, or th order arithmetic. We also prove bounds on the strength of Borel determinacy for proper class games. These results answer questions of Gitman and Hamkins.
Cite
@article{arxiv.1607.05515,
title = {Determinacy separations for class games},
author = {Sherwood Hachtman},
journal= {arXiv preprint arXiv:1607.05515},
year = {2016}
}