@article{a975b8c1-5522-3982-9018-ca5f5926d04f,
    issn = {00224812, 19435886},
    url = {http://www.jstor.org/stable/43303700},
    abstract = {We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by realtime 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 ⍵-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)).},
    author = {Olivier Finkel},
    journal = {The Journal of Symbolic Logic},
    number = {4},
    pages = {1115--1134},
    publisher = {[Association for Symbolic Logic, Cambridge University Press]},
    title = {The deteterminacy of context-free games},
    urldate = {2026-02-10},
    volume = {78},
    year = {2013},
    date-added = {2026-2-10 19:18:51 +0100}
}

@article{a975b8c1-5522-3982-9018-ca5f5926d04f, issn = {00224812, 19435886}, url = {http://www.jstor.org/stable/43303700}, abstract = {We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by realtime 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 ⍵-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)).}, author = {Olivier Finkel}, journal = {The Journal of Symbolic Logic}, number = {4}, pages = {1115--1134}, publisher = {[Association for Symbolic Logic, Cambridge University Press]}, title = {The deteterminacy of context-free games}, urldate = {2026-02-10}, volume = {78}, year = {2013}, date-added = {2026-2-10 19:18:51 +0100} }