{
  "id": "1601.04168",
  "version": "v1",
  "published": "2016-01-16T14:25:24.000Z",
  "updated": "2016-01-16T14:25:24.000Z",
  "title": "On the strength of a weak variant of the Axiom of Counting",
  "authors": [
    "Zachiri McKenzie"
  ],
  "comment": "14 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "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 $\\mathrm{NF}+\\mathrm{AxCount}_\\geq$ proves that consistency of $\\mathrm{TSTI}$, and that $\\mathrm{NFU}^{-\\mathrm{AC}}+\\mathrm{AxCount}_\\geq$ proves the consistency of $\\mathrm{NFU}^{-\\mathrm{AC}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-16T14:25:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak variant",
      "denote ronald jensens modification",
      "consistency",
      "simple theory",
      "result implies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160104168M"
    }
  }
}