{"paper":{"title":"Slow and Ordinary Provability for Peano Arithmetic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Fedor Pakhomov, Paula Henk","submitted_at":"2016-02-04T20:41:59Z","abstract_excerpt":"The notion of slow provability for Peano Arithmetic ($\\mathsf{PA}$) was introduced by S.D. Friedman, M. Rathjen, and A. Weiermann. They studied the slow consistency statement $\\mathrm{Con}_{\\mathsf{s}}$ that asserts that a contradiction is not slow provable in $\\mathsf{PA}$. They showed that the logical strength of $\\mathsf{PA}+\\mathrm{Con}_{\\mathsf{s}}$ lies strictly between that of $\\mathsf{PA}$ and $\\mathsf{PA}$ together with its ordinary consistency: $\\mathsf{PA}\\subsetneq \\mathsf{PA}+\\mathrm{Con}_{\\mathsf{s}}\\subsetneq \\mathsf{PA}+\\mathrm{Con}$.\n  This paper is a further investigation int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01822","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"}