{
  "id": "math/0404240",
  "version": "v1",
  "published": "2004-04-13T02:03:46.000Z",
  "updated": "2004-04-13T02:03:46.000Z",
  "title": "The pair $(\\aleph_n,\\aleph_0)$ may fail $\\aleph_0$--compactness",
  "authors": [
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let P be a distinguished unary predicate and K= {M: M a model of cardinality aleph_n with P^M of cardinality aleph_0}. We prove that consistently for n=4, for some countable first order theory T we have: T has no model in K whereas every finite subset of T has a model in K. We then show how we prove it also for n=2, too.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-13T02:03:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compactness",
      "countable first order theory",
      "finite subset",
      "cardinality",
      "distinguished unary predicate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4240S"
    }
  }
}