{"paper":{"title":"The Determinacy of Context-Free Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","math.LO"],"primary_cat":"cs.LO","authors_text":"IMJ), Olivier Finkel (ELM","submitted_at":"2013-12-12T07:33:31Z","abstract_excerpt":"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) Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3412","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}