{"paper":{"title":"Determinacy and J\\'onsson cardinals in $L(\\mathbb{R})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Farmer Schlutzenberg, Richard Ketchersid, Steve Jackson, W. Hugh Woodin","submitted_at":"2013-04-08T19:23:14Z","abstract_excerpt":"Assume $\\mathsf{ZF}+\\mathsf{AD}+V=L(\\mathbb{R})$ and let $\\kappa<\\Theta$ be an uncountable cardinal. We show that $\\kappa$ is J\\'onsson, and that if $\\mathrm{cof}(\\kappa)=\\omega$ then $\\kappa$ is Rowbottom. We also establish some other partition properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2323","kind":"arxiv","version":3},"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"}