{"paper":{"title":"Taking a Detour to Zero: An Alternative Formalization of Functions Beyond PR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"David M. Cerna","submitted_at":"2016-09-23T07:34:18Z","abstract_excerpt":"There are two well known systems formalizing total recursion beyond primitive recursion (\\textbf{PR}), system \\textbf{T} by G\\\"odel and system \\textbf{F} by Girard and Reynolds. system \\textbf{T} defines recursion on typed objects and can construct every function of Heyting arithmetic (\\textbf{HA}). System \\textbf{F} introduces type variables which can define the recursion of system \\textbf{T}. The result is a system as expressive as second-order Heyting arithmetic (\\textbf{HA}$_{2}$). Though, both are able to express unimaginably fast growing functions, in some applications a more flexible fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07254","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"}