{"paper":{"title":"Total Recursion over Lexicographical Orderings: Elementary Recursive Operators Beyond PR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"David Cerna","submitted_at":"2016-08-24T13:34:32Z","abstract_excerpt":"In this work we generalize primitive recursion in order to construct a hierarchy of terminating total recursive operators which we refer to as {\\em leveled primitive recursion of order $i$}($\\mathbf{PR}_{i}$). Primitive recursion is equivalent to leveled primitive recursion of order $1$ ($\\mathbf{PR}_{1}$). The functions constructable from the basic functions make up $\\mathbf{PR}_{0}$. Interestingly, we show that $\\mathbf{PR}_{2}$ is a conservative extension of $\\mathbf{PR}_{1}$. However, members of the hierarchy beyond $\\mathbf{PR}_{2}$, that is $\\mathbf{PR}_{i}$ where $i\\geq 3$, can formaliz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07163","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"}