{"paper":{"title":"Indiscernible Sequences for Extenders, and the Singular Cardinal Hypothesis","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Moti Gitik, William Mitchell","submitted_at":"1995-07-27T00:00:00Z","abstract_excerpt":"We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis.  The main result is the following theorem:\n  Theorem: Suppose $\\kappa$ is a singular strong limit cardinal and $2^\\kappa >= \\lambda$ where $\\lambda$ is not the successor of a cardinal of cofinality at most $\\kappa$.\n (i) If $\\cofinality(\\kappa)>\\gw$ then $o(\\kappa)\\ge\\lambda$.\n (ii) If $\\cofinality(\\kappa)=\\gw$ then either $o(\\kappa)\\ge\\lambda$ or $\\set{\\ga:K\\sat o(\\ga)\\ge\\ga^{+n}}$ is cofinal in $\\kappa$ for each $n\\in\\gw$.\n  In order to prove this theorem we give a d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9507214","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"}