{
  "id": "1512.08691",
  "version": "v1",
  "published": "2015-12-29T14:27:16.000Z",
  "updated": "2015-12-29T14:27:16.000Z",
  "title": "Correspondences between model theory and banach space theory",
  "authors": [
    "Karim Khanaki"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1509.03193",
  "categories": [
    "math.LO",
    "math.FA"
  ],
  "abstract": "In \\cite{K3} we pointed out the correspondence between a result of Shelah in model theory, i.e. a theory is unstable if and only if it has IP or SOP, and the well known compactness theorem of Eberlein and \\v{S}mulian in functional analysis. In this paper, we relate a {\\em natural} Banach space $V$ to a formula $\\phi(x,y)$, and show that $\\phi$ is stable (resp NIP, NSOP) if and only if $V$ is reflexive (resp Rosenthal, weakly sequentially complete) Banach space. Also, we present a proof of the Eberlein-\\v{S}mulian theorem by a model theoretic approach using Ramsey theorems which is illustrative to show some correspondences between model theory and Banach space theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-29T14:27:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "46E15",
      "46B50"
    ],
    "keywords": [
      "banach space theory",
      "model theory",
      "correspondence",
      "model theoretic approach",
      "resp rosenthal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151208691K"
    }
  }
}