{"paper":{"title":"On the strength of a weak variant of the Axiom of Counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Zachiri McKenzie","submitted_at":"2016-01-16T14:25:24Z","abstract_excerpt":"In this paper $\\mathrm{NFU}^{-\\mathrm{AC}}$ is used to denote Ronald Jensen's modification of Quine's `New Foundations' Set Theory ($\\mathrm{NF}$) fortified with a type-level pairing function but without the Axiom of Choice. The axiom $\\mathrm{AxCount}_\\geq$ is the variant of the Axiom of Counting which asserts that no finite set is smaller than its own set of singletons. This paper shows that $\\mathrm{NFU}^{-\\mathrm{AC}}+\\mathrm{AxCount}_\\geq$ proves the consistency of the Simple Theory of Types with Infinity ($\\mathrm{TSTI}$). This result implies that $\\mathrm{NF}+\\mathrm{AxCount}_\\geq$ prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04168","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"}