{"paper":{"title":"On principles between $\\Sigma_1$- and $\\Sigma_2$-induction, and monotone enumerations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Alexander P. Kreuzer, Keita Yokoyama","submitted_at":"2013-06-08T15:51:13Z","abstract_excerpt":"We show that many principles of first-order arithmetic, previously only known to lie strictly between $\\Sigma_1$-induction and $\\Sigma_2$-induction, are equivalent to the well-foundedness of $\\omega^\\omega$.\n  Among these principles are the iteration of partial functions ($P\\Sigma_1$) of H\\'ajek and Paris, the bounded monotone enumerations principle (non-iterated, BME$_1$) by Chong, Slaman, and Yang, the relativized Paris-Harrington principle for pairs, and the totality of the relativized Ackermann-P\\'eter function.\n  With this we show that the well-foundedness of $\\omega^\\omega$ is a far more"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1936","kind":"arxiv","version":5},"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"}