{"paper":{"title":"The Complexity of Infinite Computations In Models of Set Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.LO"],"primary_cat":"cs.LO","authors_text":"Olivier Finkel (ELM)","submitted_at":"2009-10-07T14:03:53Z","abstract_excerpt":"We prove the following surprising result: there exist a 1-counter B\\\"uchi automaton and a 2-tape B\\\"uchi automaton such that the \\omega-language of the first and the infinitary rational relation of the second in one model of ZFC are \\pi_2^0-sets, while in a different model of ZFC both are analytic but non Borel sets.\n  This shows that the topological complexity of an \\omega-language accepted by a 1-counter B\\\"uchi automaton or of an infinitary rational relation accepted by a 2-tape B\\\"uchi automaton is not determined by the axiomatic system ZFC.\n  We show that a similar result holds for the cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1268","kind":"arxiv","version":5},"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"}