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December 2013 The determinacy of context-free games
Olivier Finkel
J. Symbolic Logic 78(4): 1115-1134 (December 2013). DOI: 10.2178/jsl.7804050


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 $\mathcal{A}$ and a Büchi automaton $\mathcal{B}$ such that: (1) There exists a model of ZFC in which Player 2 has a winning strategy in the Wadge game $W(L(\mathcal{A}), L(\mathcal{B}))$; (2) There exists a model of ZFC in which the Wadge game $W(L(\mathcal{A}), L(\mathcal{B}))$ 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 $W(L(\mathcal{A}), L(\mathcal{B}))$.


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Olivier Finkel. "The determinacy of context-free games." J. Symbolic Logic 78 (4) 1115 - 1134, December 2013.


Published: December 2013
First available in Project Euclid: 5 January 2014

zbMATH: 1349.03038
MathSciNet: MR2909345
Digital Object Identifier: 10.2178/jsl.7804050

Keywords: 1-counter automaton , Automata and formal languages , context-free games , determinacy , effective analytic determinacy , Gale-Stewart games , independence from the axiomatic system ZFC , logic in computer science , models of set theory , Wadge games

Rights: Copyright © 2013 Association for Symbolic Logic


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Vol.78 • No. 4 • December 2013
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