{"paper":{"title":"Mice with finitely many Woodin cardinals from optimal determinacy hypotheses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ralf Schindler, Sandra M\\\"uller, W. Hugh Woodin","submitted_at":"2019-02-15T17:16:03Z","abstract_excerpt":"We prove the following result which is due to the third author. Let $n \\geq 1$. If $\\boldsymbol\\Pi^1_n$ determinacy and $\\Pi^1_{n+1}$ determinacy both hold true and there is no $\\boldsymbol\\Sigma^1_{n+2}$-definable $\\omega_1$-sequence of pairwise distinct reals, then $M_n^\\#$ exists and is $\\omega_1$-iterable. The proof yields that $\\boldsymbol\\Pi^1_{n+1}$ determinacy implies that $M_n^\\#(x)$ exists and is $\\omega_1$-iterable for all reals $x$. A consequence is the Determinacy Transfer Theorem for arbitrary $n \\geq 1$, namely the statement that $\\boldsymbol\\Pi^1_{n+1}$ determinacy implies $\\Ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05890","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"}