{"paper":{"title":"Separating Bounded Arithmetics by Herbrand Consistency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Saeed Salehi","submitted_at":"2010-08-02T05:07:52Z","abstract_excerpt":"The problem of $\\Pi_1-$separating the hierarchy of bounded arithmetic has been studied in the paper. It is shown that the notion of Herbrand Consistency, in its full generality, cannot $\\Pi_1-$separate the theory ${\\rm I\\Delta_0+\\bigwedge_j\\Omega_j}$ from ${\\rm I\\Delta_0}$; though it can $\\Pi_1-$separate ${\\rm I\\Delta_0+Exp}$ from ${\\rm I\\Delta_0}$. This extends a result of L. A. Ko{\\l}odziejczyk (2006), by showing the unprovability of the Herbrand Consistency of ${\\rm I\\Delta_0}$ in the theory ${\\rm I\\Delta_0+\\bigwedge_j\\Omega_j}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0225","kind":"arxiv","version":3},"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"}