{
  "id": "1210.7883",
  "version": "v1",
  "published": "2012-10-30T01:48:48.000Z",
  "updated": "2012-10-30T01:48:48.000Z",
  "title": "On Weak Elimination of Hyperimaginaries and its Consequences",
  "authors": [
    "Donald Brower",
    "Cameron Donnay Hill"
  ],
  "comment": "16 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We analyze the notion of weak elimination of hyperimaginaries (WEHI) in simple theories. A key observation in the analysis is a characterization of WEHI in terms of forking dependence -- a condition we dub dependence-witnessed-by-imaginaries (DWIP). Generalizing results of [1] and [3], we show that in a simple theory with WEHI, forking and thorn-forking coincide. We also show that, conversely, the equivalence of independence and thorn-independence is (almost) sufficient for WEHI. Thus, the WEHI and the statement independence = thorn-independence are morally equivalent. As a further application of our technology, we demonstrate stable forking for 1-based theories of finite SU-rank that have WEHI.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-30T01:48:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak elimination",
      "hyperimaginaries",
      "consequences",
      "simple theory",
      "dub dependence-witnessed-by-imaginaries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7883B"
    }
  }
}