{
  "id": "1812.02840",
  "version": "v1",
  "published": "2018-12-06T22:45:02.000Z",
  "updated": "2018-12-06T22:45:02.000Z",
  "title": "On the undefinability of Tsirelson's space and its descendants",
  "authors": [
    "Peter Casazza",
    "Jose Iovino"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove that Tsirelson's space cannot be defined explicitly from the classical Banach sequence spaces. We also prove that any Banach space that is explicitly definable from a class of spaces that contain $\\ell_p$ or $c_0$ must contain $\\ell_p$ or $c_0$ as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-06T22:45:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tsirelsons space",
      "undefinability",
      "descendants",
      "classical banach sequence spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}