{"paper":{"title":"Comparing the strength of diagonally non-recursive functions in the absence of $\\Sigma^0_2$ induction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Fran\\c{c}ois G. Dorais, Jeffry L. Hirst, Paul Shafer","submitted_at":"2014-01-16T03:51:05Z","abstract_excerpt":"We prove that the statement \"there is a $k$ such that for every $f$ there is a $k$-bounded diagonally non-recursive function relative to $f$\" does not imply weak K\\\"onig's lemma over $\\mathrm{RCA}_0 + \\mathrm{B}\\Sigma^0_2$. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every $k$-bounded diagonally non-recursive function computes a $2$-bounded diagonally non-recursive function may fail in the absence of $\\mathrm{I}\\Sigma^0_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3823","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"}