The Determinacy of Context-Free Games
Abstract
We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal assumption. We show also that the determinacy of Wadge games between two players in charge of omega-languages accepted by 1-counter B\"uchi automata is equivalent to the (effective) analytic Wadge determinacy. Using some results of set theory we prove that one can effectively construct a 1-counter B\"uchi automaton A and a B\"uchi automaton B such that: (1) There exists a model of ZFC in which Player 2 has a winning strategy in the Wadge game W(L(A), L(B)); (2) There exists a model of ZFC in which the Wadge game W(L(A), L(B)) is not determined. Moreover these are the only two possibilities, i.e. there are no models of ZFC in which Player 1 has a winning strategy in the Wadge game W(L(A), L(B)).
Keywords
Cite
@article{arxiv.1312.3412,
title = {The Determinacy of Context-Free Games},
author = {Olivier Finkel},
journal= {arXiv preprint arXiv:1312.3412},
year = {2013}
}
Comments
This paper is an extended version of a STACS 2012 conference paper [arXiv:1112.1186]. It will appear in the Journal of Symbolic Logic