{
  "id": "1409.8172",
  "version": "v1",
  "published": "2014-09-29T16:15:54.000Z",
  "updated": "2014-09-29T16:15:54.000Z",
  "title": "Some Banach spaces added by a Cohen real",
  "authors": [
    "Mirna Džamonja"
  ],
  "comment": "preprint. arXiv admin note: substantial text overlap with arXiv:1308.3640",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study certain Banach spaces that are added in the extension by one Cohen real. Specifically, we show that adding just one Cohen real to any model adds a Banach space of density $\\aleph_1$ which does not embed into any such space in the ground model such a Banach space can be chosen to be UG This has consequences on the the isomorphic universality number for Banach spaces of density $\\aleph_1$, which is hence equal to $\\aleph_2$ in the standard Cohen model and the same is true for UG spaces. Analogous universality results for Banach spaces are true for other cardinals, by a different proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-29T16:15:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cohen real",
      "banach spaces",
      "isomorphic universality number",
      "standard cohen model",
      "model adds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.8172D"
    }
  }
}