{"paper":{"title":"Positional strategies in long Ehrenfeucht-Fraiss\\'e games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Boban Velickovic, Jouko V\\\"a\\\"an\\\"anen, Saharon Shelah","submitted_at":"2013-08-01T11:31:20Z","abstract_excerpt":"We prove that it is relatively consistent with ZF + CH that there exist two models of cardinality \\aleph_2 such that the second player has a winning strategy in the Ehrenfeucht-Fra\\\"iss\\'e-game of length \\omega_1 but there is no \\sigma-closed back-and-forth set for the two models. If CH fails, no such pairs of models exist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0156","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"}