{
  "id": "1812.09378",
  "version": "v1",
  "published": "2018-12-21T21:42:10.000Z",
  "updated": "2018-12-21T21:42:10.000Z",
  "title": "Forking, Imaginaries and other features of ACFG",
  "authors": [
    "Christian d'Elbée"
  ],
  "comment": "31 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study the generic theory of algebraically closed fields of fixed positive characteristic with a predicate for an additive subgroup, called $\\mathrm{ACFG}$. This theory was introduced recently as a new example of $\\mathrm{NSOP}_1$ non simple theory. In this paper we describe more features of $\\mathrm{ACFG}$, such as imaginaries. We also study various independence relations in $\\mathrm{ACFG}$, such as Kim-independence or forking independence, and describe interactions between them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-21T21:42:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "imaginaries",
      "non simple theory",
      "generic theory",
      "independence relations",
      "positive characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}