{"paper":{"title":"Borel* Sets in the Generalised 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":"2012-09-18T12:46:38Z","abstract_excerpt":"We start by giving a survey to the theory of Borel*(\\kappa) sets in the generalized Baire space Baire({\\kappa}) = {\\kappa}^{\\kappa}. In particular we look at the relation of this complexity class to other complexity classes which we denote by Borel({\\kappa}), \\Delta^1_1({\\kappa}) and {\\Sigma}^1_1({\\kappa}) and the connections between Borel*(\\kappa)-sets and the infinitely deep language M_{{\\kappa}^+{\\kappa}}. In the end of the paper we prove the consistency of Borel*(\\kappa) \\ne {\\Sigma}^1_1({\\kappa})."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3933","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"}