{
  "id": "2107.05197",
  "version": "v1",
  "published": "2021-07-12T05:14:08.000Z",
  "updated": "2021-07-12T05:14:08.000Z",
  "title": "Density of compressible types and some consequences",
  "authors": [
    "Martin Bays",
    "Itay Kaplan",
    "Pierre Simon"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We study compressible types in the context of (local and global) NIP. By extending a result in machine learning theory (the existence of a bound on the recursive teaching dimension), we prove density of compressible types. Using this, we obtain explicit uniform honest definitions for NIP formulas (answering a question of Eshel and the second author), and build compressible models in countable NIP theories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-12T05:14:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C95",
      "03C50"
    ],
    "keywords": [
      "consequences",
      "explicit uniform honest definitions",
      "nip formulas",
      "countable nip theories",
      "machine learning theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}