{"paper":{"title":"End-extensions of models of weak arithmetic from complexity-theoretic containments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Leszek Aleksander Ko{\\l}odziejczyk","submitted_at":"2014-11-25T13:39:51Z","abstract_excerpt":"We prove that if the linear-time and polynomial-time hierarchies coincide, then every model of $\\Pi_1(\\mathbb{N}) + \\neg \\Omega_1$ has a proper end-extension to a model of $\\Pi_1(\\mathbb{N})$, and so $\\Pi_1(\\mathbb{N}) + \\neg \\Omega_1 \\vdash \\mathrm{B}\\Sigma_1$. Under an even stronger complexity-theoretic assumption which nevertheless seems hard to disprove using present-day methods, $\\Pi_1(\\mathbb{N}) + \\neg \\mathrm{Exp} \\vdash \\mathrm{B}\\Sigma_1$. Both assumptions can be modified to versions which make it possible to replace $\\Pi_1(\\mathbb{N})$ by $\\mathrm{I}\\Delta_0$ as the base theory.\n  W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6864","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"}