{"paper":{"title":"Consecutive singular cardinals and the continuum function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Arthur W. Apter, Brent Cody","submitted_at":"2011-12-08T17:29:32Z","abstract_excerpt":"We show that from a supercompact cardinal \\kappa, there is a forcing extension V[G] that has a symmetric inner model N in which ZF + not AC holds, \\kappa\\ and \\kappa^+ are both singular, and the continuum function at \\kappa\\ can be precisely controlled, in the sense that the final model contains a sequence of distinct subsets of \\kappa\\ of length equal to any predetermined ordinal. We also show that the above situation can be collapsed to obtain a model of ZF + not AC_\\omega\\ in which either (1) aleph_1 and aleph_2 are both singular and the continuum function at aleph_1 can be precisely contro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1890","kind":"arxiv","version":2},"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"}