{"paper":{"title":"Easton functions and supercompactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Brent Cody, Radek Honzik, Sy-David Friedman","submitted_at":"2013-11-01T20:56:13Z","abstract_excerpt":"Suppose $\\kappa$ is $\\lambda$-supercompact witnessed by an elementary embedding $j:V\\rightarrow M$ with critical point $\\kappa$, and further suppose that $F$ is a function from the class of regular cardinals to the class of cardinals satisfying the requirements of Easton's theorem: (1) $\\forall\\alpha$ $\\alpha<\\textrm{cf}(F(\\alpha))$ and (2) $\\alpha<\\beta$ $\\Longrightarrow$ $F(\\alpha)\\leq F(\\beta)$. In this article we address the question: assuming GCH, what additional assumptions are necessary on $j$ and $F$ if one wants to be able to force the continuum function to agree with $F$ globally, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0303","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"}