{
  "id": "math/0009087",
  "version": "v2",
  "published": "2000-09-08T13:37:11.000Z",
  "updated": "2011-04-14T23:40:19.000Z",
  "title": "On triangleleft^*-maximality",
  "authors": [
    "Mirna Džamonja",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "This paper investigates a connection between the ordering triangleleft^ast among theories in model theory and the (N)SOP_n hierarchy of Shelah. It introduces two properties which are natural extensions of this hierarchy, called SOP_2 and SOP_1, and gives a strong connection between SOP_1 and the maximality in Keisler ordering. Together with the known results about the connection between the (N)SOP_n hierarchy and the existence of universal models in the absence of GCH, the paper provides a step toward the classification of unstable theories without the strict order property.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-14T23:40:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strict order property",
      "model theory",
      "natural extensions",
      "strong connection",
      "universal models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9087D"
    }
  }
}