{"paper":{"title":"The failure of GCH at a degree of supercompactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Brent Cody","submitted_at":"2011-10-24T22:20:49Z","abstract_excerpt":"We determine the large cardinal consistency strength of the existence of a $\\lambda$-supercompact cardinal $\\kappa$ such that GCH fails at $\\lambda$. Indeed, we show that the existence of a $\\lambda$-supercompact cardinal $\\kappa$ such that $2^\\lambda \\geq \\theta$ is equiconsistent with the existence of a $\\lambda$-supercompact cardinal that is also $\\theta$-tall. We also prove some basic facts about the large cardinal notion of tallness with closure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5365","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"}