{"paper":{"title":"First- and Second-Order Models of Recursive Arithmetics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"J\\'an K\\v{l}uka, Paul J. Voda","submitted_at":"2017-05-15T21:29:43Z","abstract_excerpt":"We study a quadruple of interrelated subexponential subsystems of arithmetic WKL$_0^-$, RCA$^-_0$, I$\\Delta_0$, and $\\Delta$RA$_1$, which complement the similarly related quadruple WKL$_0$, RCA$_0$, I$\\Sigma_1$, and PRA studied by Simpson, and the quadruple WKL$_0^\\ast$, RCA$_0^\\ast$, I$\\Delta_0$(exp), and EFA studied by Simpson and Smith. We then explore the space of subexponential arithmetic theories between I$\\Delta_0$ and I$\\Delta_0$(exp). We introduce and study first- and second-order theories of recursive arithmetic $A$RA$_1$ and $A$RA$_2$ capable of characterizing various computational "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05459","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"}