{"paper":{"title":"Determinacy of Refinements to the Difference Hierarchy of Co-analytic Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Chris Le Sueur","submitted_at":"2014-11-04T23:02:16Z","abstract_excerpt":"In this paper we develop a technique for proving determinacy of classes of the form $\\omega^2-\\Pi^1_1+\\Gamma$ (a refinement of the difference hierarchy on the co-analytic sets lying between $\\omega^2-\\Pi^1_1$ and $(\\omega^2+1)-\\Pi^1_1$) from weak principles, establishing upper bounds for the determinacy-strength of the classes $\\omega^2-\\Pi^1_1+\\Sigma^0_\\alpha$ for all computable $\\alpha$ and of $\\omega^2-\\Pi^1_1+\\Delta^1_1$. This bridges the gap between previously known hypotheses implying determinacy in this region."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1106","kind":"arxiv","version":2},"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"}