{"paper":{"title":"Easton's Theorem for Ramsey and Strongly Ramsey cardinals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Brent Cody, Victoria Gitman","submitted_at":"2012-09-05T22:23:56Z","abstract_excerpt":"We show that, assuming GCH, if $\\kappa$ is a Ramsey or a strongly Ramsey cardinal and $F$ is a class function on the regular cardinals having a closure point at $\\kappa$ and obeying the constraints of Easton's theorem, namely, $F(\\alpha)\\leq F(\\beta)$ for $\\alpha\\leq\\beta$ and $\\alpha<\\cf(F(\\alpha))$, then there is a cofinality preserving forcing extension in which $\\kappa$ remains Ramsey or strongly Ramsey respectively and $2^\\delta=F(\\delta)$ for every regular cardinal $\\delta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1133","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"}