{"paper":{"title":"On the Singular Cardinal Hypothesis","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"William J. Mitchell","submitted_at":"1992-04-06T00:00:00Z","abstract_excerpt":"We use the core model for sequences of measures to prove a new lower bound for the consistency strength of the failure of the SCH:\n  THEOREM\n (i) If there is a singular strong limit cardinal $\\kappa$ such that $2^\\kappa > kappa^+$ then there is an inner model with a cardinal $\\kappa$ such that for all ordinals $\\alpha<\\kappa$ there is an ordinal $\\nu < \\kappa$ with $o(\\nu) > \\alpha$.\n (ii) If there is a singular strong limit cardinal $\\kappa$ of uncountable cofinality such that $2^\\kappa > \\kappa^+$ then there is an inner model with $o(\\kappa) = \\kappa^{++}$.\n  Since this paper was originally "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9204202","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"}