{
  "id": "math/0009080",
  "version": "v1",
  "published": "2000-09-07T20:18:27.000Z",
  "updated": "2000-09-07T20:18:27.000Z",
  "title": "A Note on Extensions of Infinitary Logic",
  "authors": [
    "Saharon Shelah",
    "Jouko Väänänen"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that a strong form of the so called Lindstrom's Theorem fails to generalize to extensions of L_{kappa,omega} and L_{kappa,kappa}: For weakly compact kappa there is no strongest extension of L_{kappa,omega} with the (kappa,kappa)-compactness property and the Lowenheim-Skolem theorem down to kappa. With an additional set-theoretic assumption, there is no strongest extension of L_{kappa,kappa} with the (kappa,kappa)-compactness property and the Lowenheim-Skolem theorem down to <kappa.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-09-07T20:18:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinitary logic",
      "lowenheim-skolem theorem",
      "strongest extension",
      "lindstroms theorem fails",
      "additional set-theoretic assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9080S"
    }
  }
}