{"paper":{"title":"Easton's Theorem in the presence of Woodin cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Brent Cody","submitted_at":"2012-07-24T20:52:41Z","abstract_excerpt":"Under the assumption that $\\delta$ is a Woodin cardinal and $\\GCH$ holds, I show that if $F$ is any class function from the regular cardinals to the cardinals such that (1) $\\kappa<\\cf(F(\\kappa))$, (2) $\\kappa<\\lambda$ implies $F(\\kappa)\\leq F(\\lambda)$, and (3) $\\delta$ is closed under $F$, then there is a cofinality-preserving forcing extension in which $2^\\gamma= F(\\gamma)$ for each regular cardinal $\\gamma<\\delta$, and in which $\\delta$ remains Woodin. Unlike the analogous results for supercompact cardinals [Men76] and strong cardinals [FH08], there is no requirement that the function $F$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5822","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"}