{"paper":{"title":"On \\Sigma^1_1-complete Equivalence Relations on the Generalized Baire Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tapani Hyttinen, Vadim Kulikov","submitted_at":"2012-09-18T12:45:32Z","abstract_excerpt":"Working with uncountable structures of fixed cardinality, we investigate the complexity of certain equivalence relations and show that if V = L, then many of them are \\Sigma^1_1-complete, in particular the isomorphism relation of dense linear orders.\n  Then we show that it is undecidable in ZFC whether or not the isomorphism relation of a certain well behaved theory (stable, NDOP, NOTOP) is \\Sigma^1_1-complete (it is, if V = L, but can be forced not to be)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3932","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"}