{
  "id": "math/9207205",
  "version": "v1",
  "published": "1992-07-31T00:00:00.000Z",
  "updated": "1992-07-31T00:00:00.000Z",
  "title": "Remark on the Failure of Martin's Axiom",
  "authors": [
    "Avner Landver"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let m be the least cardinal k such that MA(k) fails. The only known model for \"m is singular\" was constructed by Kunen. In Kunen's model cof(m)=omega_1. It is unknown whether \"omega_1 < cof(m) < m\" is consistent. The purpose of this paper is to present a proof of Kunen's result and to identify the difficulties of generalizing this result to an arbitrary uncountable cofinality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-07-31T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "martins axiom",
      "kunens model",
      "kunens result",
      "arbitrary uncountable cofinality",
      "consistent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math......7205L"
    }
  }
}