{
  "id": "1404.2776",
  "version": "v2",
  "published": "2014-04-10T11:48:26.000Z",
  "updated": "2019-08-28T18:35:06.000Z",
  "title": "Adding a random real number and its effect on Martin's axiom",
  "authors": [
    "Joan Bagaria",
    "Saharon Shelah"
  ],
  "comment": "Wrong proof. arXiv:1502.05500 contains the corrected version",
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that adding a random real number destroys a large fragment of Martin's axiom, namely Martin's axiom for partial orders that have precalibre-$\\aleph_1$, thus answering an old question of J. Roitman [9]. We also answer a question of J. Steprans and S. Watson [13] by showing that, by a forcing that preserves cardinals, one can destroy the precalibre-$\\aleph_1$ property of a partial ordering while preserving its ccc-ness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-10T11:48:26.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2019-08-28T18:35:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03Exx",
      "03E50",
      "03E57"
    ],
    "keywords": [
      "martins axiom",
      "random real number destroys",
      "large fragment",
      "partial orders",
      "old question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2776B"
    }
  }
}