{
  "id": "math/9706225",
  "version": "v1",
  "published": "1997-06-15T00:00:00.000Z",
  "updated": "1997-06-15T00:00:00.000Z",
  "title": "Stationary sets and infinitary logic",
  "authors": [
    "Saharon Shelah",
    "Jouko Väänänen"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let K^0_lambda be the class of structures < lambda,<,A>, where A subseteq lambda is disjoint from a club, and let K^1_lambda be the class of structures < lambda,<,A>, where A subseteq lambda contains a club. We prove that if lambda = lambda^{< kappa} is regular, then no sentence of L_{lambda^+ kappa} separates K^0_lambda and K^1_lambda. On the other hand, we prove that if lambda = mu^+, mu = mu^{< mu}, and a forcing axiom holds (and aleph_1^L= aleph_1 if mu = aleph_0), then there is a sentence of L_{lambda lambda} which separates K^0_lambda and K^1_lambda .",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-06-15T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinitary logic",
      "stationary sets",
      "subseteq lambda contains",
      "structures",
      "forcing axiom holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997math......6225S"
    }
  }
}