{
  "id": "2303.04125",
  "version": "v2",
  "published": "2023-03-07T18:39:28.000Z",
  "updated": "2023-03-27T04:56:04.000Z",
  "title": "An NIP-like Notion in Abstract Elementary Classes",
  "authors": [
    "Wentao Yang"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "This paper is a contribution to \"neo-stability\" type of result for abstract elementary classes. Under certain set theoretic assumptions, we propose a definition and a characterization of NIP in AECs. The class of AECs with NIP properly contains the class of stable AECs. We show that for an AEC $K$ and $\\lambda\\geq LS(K)$, $K_\\lambda$ is NIP if and only if there is a notion of nonforking on it which we call a w*-good frame. On the other hand, the negation of NIP leads to being able to encode subsets.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-03-27T04:56:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C48",
      "03C52"
    ],
    "keywords": [
      "abstract elementary classes",
      "nip-like notion",
      "set theoretic assumptions",
      "nip properly contains",
      "encode subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}