{
  "id": "1712.06503",
  "version": "v1",
  "published": "2017-12-18T16:34:16.000Z",
  "updated": "2017-12-18T16:34:16.000Z",
  "title": "Neutrally Expandable Models of Arithmetic",
  "authors": [
    "Athar Abdul-Quader",
    "Roman Kossak"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "A subset of a model of ${\\sf PA}$ is called neutral if it does not change the $\\mathrm{dcl}$ relation. A model with undefinable neutral classes is called neutrally expandable. We study the existence and non-existence of neutral sets in various models of ${\\sf PA}$. We show that cofinal extensions of prime models are neutrally expandable, and $\\omega_1$-like neutrally expandable models exist, while no recursively saturated model is neutrally expandable. We also show that neutrality is not a first-order property. In the last section, we study a local version of neutral expandability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-18T16:34:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C62",
      "03H15"
    ],
    "keywords": [
      "neutrally expandable models",
      "arithmetic",
      "neutral expandability",
      "neutral sets",
      "undefinable neutral classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}