{"paper":{"title":"The covering lemma up to a Woodin cardinal","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ernest Schimmerling, John R. Steel, William J. Mitchell","submitted_at":"1997-02-18T00:00:00Z","abstract_excerpt":"A cardinal kappa is countably closed if mu^omega < kappa whenever mu < kappa.\n  Assume that there is no inner model with a Woodin cardinal and that every set has a sharp.  Let K be the core model.  Assume that kappa is a countably closed cardinal and that alpha is a successor cardinal of K with kappa < alpha < kappa^+.  Then cf( alpha ) = kappa.  In particular, K computes successors of countably closed singular cardinals correctly.\n  (The hypothesis of countable closure is not required; see \"Weak covering without countable closure\", W. J. Mitchell and E. Schimmerling, Math. Res. Lett., Vol. 2,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9702207","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"}