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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","authors_text":"Moti Gitik, William Mitchell","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1995-07-27T00:00:00Z","title":"Indiscernible Sequences for Extenders, and the Singular Cardinal Hypothesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9507214","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:82fa03770a3353b540655e84f709310ed8c9498fd6806e7f54bddb4418c68bd1","target":"record","created_at":"2026-05-18T01:05:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0783708ee19a33d023c007ef0d455da4ab57d2d1e478791ab68efa714f25f760","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-07-27T00:00:00Z","title_canon_sha256":"70409033dfccaebfc6834b120bf7927f4e8eb98405162103ca00fa3a3c43497f"},"schema_version":"1.0","source":{"id":"math/9507214","kind":"arxiv","version":1}},"canonical_sha256":"2659b2b6e3bf8058d268e329cbe18a8b281dacbdce7c1c3bd796309008d76271","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2659b2b6e3bf8058d268e329cbe18a8b281dacbdce7c1c3bd796309008d76271","first_computed_at":"2026-05-18T01:05:48.497133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:48.497133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zrvc4oomj8XodVM+OX3QsYopkda5U2Wn1L8XfeTyFawWNsapK/U35GUI726G5RyOWu4Df077eO8EmKv+qWi1AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:48.497602Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9507214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82fa03770a3353b540655e84f709310ed8c9498fd6806e7f54bddb4418c68bd1","sha256:8cfde066c55f03ff956c8bba79accae326782e3e37aea5bd8a8f0f713f4c2e79"],"state_sha256":"bd09fe299e282c39d08668f8c72892d9757f93e6b8707f6ea0e9d27ac9a51078"}