{
  "id": "0906.3120",
  "version": "v8",
  "published": "2009-06-17T09:32:29.000Z",
  "updated": "2010-09-25T14:17:44.000Z",
  "title": "$σ$-Set Theory: Introduction to the concepts of $σ$-antielement, $σ$-antiset and Integer Space",
  "authors": [
    "Ivan Gatica Araus"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In this paper we develop a theory called $\\sigma$-Set Theory, in which we present an axiom system developed from the study of Set Theories of Zermelo-Fraenkel, Neumann-Bernays-Godel and Morse-Kelley. In $\\sigma$-Set Theory, we present the proper existence of objects called $\\sigma$-antielement, $\\sigma$-antiset, natural numbers, antinatural numbers and generated $\\sigma$-set by two $\\sigma$-sets, from which we obtain, among other things, a commutative non-associative algebraic structure called Integer Space $3^{X}$, which corresponds to the algebraic completion of $2^{X}$.",
  "revisions": [
    {
      "version": "v8",
      "updated": "2010-09-25T14:17:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "set theory",
      "integer space",
      "antielement",
      "introduction",
      "algebraic completion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.3120G"
    }
  }
}