{"paper":{"title":"Combinatorial principles equivalent to weak induction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Arno Pauly, Caleb Davis, Denis R. Hirschfeldt, Jake Pardo, Jeffry L. Hirst, Keita Yokoyama","submitted_at":"2018-12-24T15:51:00Z","abstract_excerpt":"We consider two combinatorial principles, ${\\sf{ERT}}$ and ${\\sf{ECT}}$. Both are easily proved in ${\\sf{RCA}}_0$ plus ${\\Sigma^0_2}$ induction. We give two proofs of ${\\sf{ERT}}$ in ${\\sf{RCA}}_0$, using different methods to eliminate the use of ${\\Sigma^0_2}$ induction. Working in the weakened base system ${\\sf{RCA}}_0^*$, we prove that ${\\sf{ERT}}$ is equivalent to ${\\Sigma^0_1}$ induction and ${\\sf{ECT}}$ is equivalent to ${\\Sigma^0_2}$ induction. We conclude with a Weihrauch analysis of the principles, showing ${\\sf{ERT}} {\\equiv_{\\rm W}} {\\sf{LPO}}^* {<_{\\rm W}}{{\\sf{TC}}_{\\mathbb N}}^* "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09943","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"}