{"paper":{"title":"Absoluteness via Resurrection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Giorgio Audrito, Matteo Viale","submitted_at":"2014-04-08T12:59:10Z","abstract_excerpt":"The resurrection axioms are forcing axioms introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Velickovi\\'c. We introduce a stronger form of resurrection axioms (the \\emph{iterated} resurrection axioms $\\textrm{RA}_\\alpha(\\Gamma)$ for a class of forcings $\\Gamma$ and a given ordinal $\\alpha$), and show that $\\textrm{RA}_\\omega(\\Gamma)$ implies generic absoluteness for the first-order theory of $H_{\\gamma^+}$ with respect to forcings in $\\Gamma$ preserving the axiom, where $\\gamma=\\gamma_\\Gamma$ is a cardinal which depends on $\\Gamma$ ($\\gamma_\\Gamma=\\omega_1$ if $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2111","kind":"arxiv","version":4},"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"}