{
  "id": "math/0406543",
  "version": "v1",
  "published": "2004-06-26T19:12:03.000Z",
  "updated": "2004-06-26T19:12:03.000Z",
  "title": "The Geometry of Linear Regular Types",
  "authors": [
    "Tristram de Piro"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "This paper is concerned with extending results from \"The Geometry of 1-Based Minimal Types\" by Kim and the present author. We work in the more general context of the solution set D of a regular Lascar Strong Type defined over the empty set in a simple theory T. In Pillay's book \"Geometric Stability Theory\", a notion of p-weight is developed for regular types in stable theories. Here we show that the corresponding notion holds in simple theories and give a geometric analysis of associated structures G(D) and G(D)(large), the former of which appears in the above paper. We show that D is linear iff G(D) and G(D)(large) (localized, respectively) are both modular with respect to the p-closure operator. Finally, we show that modularity of G(D)(large) provides a local analogue of 1-basedness for the theory T.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-26T19:12:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear regular types",
      "simple theory",
      "geometric stability theory",
      "regular lascar strong type",
      "local analogue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6543D"
    }
  }
}