{
  "id": "2011.03923",
  "version": "v1",
  "published": "2020-11-08T08:32:43.000Z",
  "updated": "2020-11-08T08:32:43.000Z",
  "title": "An introduction to the Scott complexity of countable structures and a survey of recent results",
  "authors": [
    "Matthew Harrison-Trainor"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Every countable structure has a sentence of the infinitary logic $\\mathcal{L}_{\\omega_1 \\omega}$ which characterizes that structure up to isomorphism among countable structures. Such a sentence is called a Scott sentence, and can be thought of as a description of the structure. The least complexity of a Scott sentence for a structure can be thought of as a measurement of the complexity of describing the structure. We begin with an introduction to the area, with short and simple proofs where possible, followed by a survey of recent advances.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-08T08:32:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "countable structure",
      "scott complexity",
      "introduction",
      "scott sentence",
      "infinitary logic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}