{
  "id": "math/9602216",
  "version": "v2",
  "published": "1996-02-15T00:00:00.000Z",
  "updated": "2023-05-18T13:38:36.000Z",
  "title": "Categoricity and amalgamation for AEC and $ κ$ measurable",
  "authors": [
    "Oren Kolman",
    "Saharon Shelah"
  ],
  "comment": "We now use the framework of AECs rather than models of a fixed theory",
  "journal": "[Sh:362]: Fund. Math. 151 (1996), 209--240",
  "categories": [
    "math.LO"
  ],
  "abstract": "In the original version of this paper, we assume a theory $T$ that the logic $\\mathbb L _{\\kappa, \\aleph_{0}}$ is categorical in a cardinal $\\lambda > \\kappa$, and $\\kappa$ is a measurable cardinal. There we prove that the class of model of $T$ of cardinality $<\\lambda$ (but $\\geq |T|+\\kappa$) has the amalgamation property; this is a step toward understanding the character of such classes of models. In this revised version we replaced the class of models of $T$ by $\\mathfrak k$, an AEC (abstract elementary class) which has LS-number ${<} \\, \\kappa,$ or at least which behave nicely for ultrapowers by $D$, a normal ultra-filter on $\\kappa$. Presently sub-section \\S1A deals with $T \\subseteq \\mathbb L_{\\kappa^{+}, \\aleph_{0}}$ (and so does a large part of the introduction and little in the rest of \\S1), but otherwise, all is done in the context of AEC.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-02-15T00:00:00.000Z",
      "title": "Categoricity of theories in L_{kappa, omega}, when kappa is a measurable cardinal. Part 1",
      "abstract": "We assume a theory T in the logic L_{kappa omega} is categorical in a cardinal lambda >= kappa, and kappa is a measurable cardinal. Here we prove that the class of model of T of cardinality < lambda (but >= |T|+ kappa) has the amalgamation property; this is a step toward understanding the character of such classes of models.",
      "comment": null,
      "journal": "Fund. Math. 151 (1996), 209--240",
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2023-05-18T13:38:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C48",
      "03C45",
      "03C55",
      "03C75",
      "03E05",
      "03E55"
    ],
    "keywords": [
      "measurable cardinal",
      "categoricity",
      "cardinal lambda",
      "amalgamation property",
      "cardinality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1996math......2216K"
    }
  }
}