{
  "id": "0807.4836",
  "version": "v1",
  "published": "2008-07-30T19:53:37.000Z",
  "updated": "2008-07-30T19:53:37.000Z",
  "title": "Paradigms-Shift in Set Theory",
  "authors": [
    "Werner DePauli-Schimanovich"
  ],
  "comment": "18 pages, no figures",
  "categories": [
    "math.LO"
  ],
  "abstract": "In this article the author claims that there is a paradigm shift from ZFC to NFUM and further to NACT - due to philosophical reasons, not mathematical ones. The goal is to construct systems where every \"Not-Properclass\" is a set! With help of Non-Monotonic Logic, the consistent systems NACT-MoonW, NACT*W, and NACT-SunW are producing \"largest possible universes\" of sets. Using self-evident philosophical principles, three approximations are suggested: NACT+NFUM-closed (to NACT*), NACT&ZFC4+(GCH) (also to NACT*) and NACT-NFUM (to NACT-Sun). Also the system NACT[&ZFC4-closed]+(FCA) is considered. NFUM = NFU with (AC) and measurable properclass Ord. NFUM-closed is NFUM where the set-constituting formulas Ai in the set operator need not only to be stratified but also to be made parameter-free (i.e., have only x as free variable over which the set is comprehended). In other formulas, free variables are allowed. Keywords: Set Theory, ZFC, Naive Set Theory, Predicate-Extension, Church Schema of Comprehension, NF, NFUM, Stratification, Universal Sets, Eliminative Class Theory, NBG, NACT (= Naive Axiomatic Class Theory), NACT-Sun, NACT-Moon, NACT-Star, NACT+NFUM-closed, ZFCK, NACT+NFUM, (GCH), (FCA) [= Finite or Countable Anti-Thesis], NACT+ZFC4+(GCH), NACT[+ZFC4-[closed]+(FCA).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-30T19:53:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "set theory",
      "paradigms-shift",
      "consistent systems nact-moonw",
      "naive axiomatic class theory",
      "self-evident philosophical principles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.4836D"
    }
  }
}