{
  "id": "2011.04034",
  "version": "v1",
  "published": "2020-11-08T17:32:27.000Z",
  "updated": "2020-11-08T17:32:27.000Z",
  "title": "A Strictly $ \\text{NSOP}_3 $ Theory",
  "authors": [
    "Massoud Pourmahdian",
    "Ali N. Valizadeh"
  ],
  "comment": "23 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We define the new notion of a $ \\mu$-uniformly-counter-collapsed structure using which we introduce a theory $ \\mathbb{T}_\\mu $ serving as the first example of a strictly $ \\text{NSOP}_3 $ theory. This answers a question posed in [DS04] and reappeared in [SU08] and [MS16]. The existence of such a theory provides a better understanding of the hierarchy of unstable theories without the strict order property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-08T17:32:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45"
    ],
    "keywords": [
      "strict order property",
      "first example",
      "unstable theories",
      "uniformly-counter-collapsed structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}