{"paper":{"title":"On sequents of $\\Sigma$ formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andre Kornell","submitted_at":"2017-04-26T15:07:29Z","abstract_excerpt":"We investigate the position that foundational theories should be modelled on ordinary computability. In this context, we investigate the metamathematics of $\\Sigma$ formulas. We consider theories whose axioms are implications between $\\Sigma$ formulas, and we show that arbitrarily strong such theories prove their own correctness. We also show that a natural extension of such a theory proves the validity of intuitionistic reasoning for that theory. Finally, we show the equivalence of two completeness principles appropriate to a potentialist conception of the universe of sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08155","kind":"arxiv","version":4},"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"}