{"paper":{"title":"Collapsing the cardinals of $HOD$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"James Cummings, Mohammad Golshani, Sy David Friedman","submitted_at":"2016-01-14T04:30:43Z","abstract_excerpt":"Assuming that $GCH$ holds and $\\kappa$ is $\\kappa^{+3}$-supercompact, we construct a generic extension $W$ of $V$ in which $\\kappa$ remains strongly inaccessible and $(\\alpha^+)^{HOD} < \\alpha^+$ for every infinite cardinal $\\alpha < \\kappa$. In particular the rank-initial segment $W_\\kappa$ is a model of ZFC in which $(\\alpha^+)^{HOD} < \\alpha^+$ for every infinite cardinal $\\alpha$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03482","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"}