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 Büchi 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 Büchi 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 Büchi automaton A and a Büchi 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)).
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Contributor : Olivier Finkel <>
Submitted on : Tuesday, December 10, 2013 - 6:31:23 PM
Last modification on : Sunday, March 31, 2019 - 1:22:32 AM
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  • HAL Id : hal-00916865, version 1
  • ARXIV : 1312.3412

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Olivier Finkel. The Determinacy of Context-Free Games. The Journal of Symbolic Logic, Association for Symbolic Logic, 2013, 78 (4), pp.1115-1134. ⟨hal-00916865⟩

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