{
  "id": "math/9305204",
  "version": "v1",
  "published": "1993-05-15T00:00:00.000Z",
  "updated": "1993-05-15T00:00:00.000Z",
  "title": "The Ehrenfeucht-Fraisse-game of length omega_1",
  "authors": [
    "Alan H. Mekler",
    "Saharon Shelah",
    "Jouko Väänänen"
  ],
  "journal": "Trans. Amer. Math. Soc. 339 (1993), 567--580",
  "categories": [
    "math.LO"
  ],
  "abstract": "Let (A) and (B) be two first order structures of the same vocabulary. We shall consider the Ehrenfeucht-Fra{i}sse-game of length omega_1 of A and B which we denote by G_{omega_1}(A,B). This game is like the ordinary Ehrenfeucht-Fraisse-game of L_{omega omega} except that there are omega_1 moves. It is clear that G_{omega_1}(A,B) is determined if A and B are of cardinality <= aleph_1. We prove the following results: Theorem A: If V=L, then there are models A and B of cardinality aleph_2 such that the game G_{omega_1}(A,B) is non-determined. Theorem B: If it is consistent that there is a measurable cardinal, then it is consistent that G_{omega_1}(A,B) is determined for all A and B of cardinality <= aleph_2. Theorem C: For any kappa >= aleph_3 there are A and B of cardinality kappa such that the game G_{omega_1}(A,B) is non-determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1993-05-15T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first order structures",
      "ordinary ehrenfeucht-fraisse-game",
      "cardinality kappa",
      "vocabulary"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1993math......5204M"
    }
  }
}