{
  "id": "2212.03677",
  "version": "v1",
  "published": "2022-12-07T14:45:59.000Z",
  "updated": "2022-12-07T14:45:59.000Z",
  "title": "Compactness in Team Semantics",
  "authors": [
    "Joni Puljujärvi",
    "Davide Emilio Quadrellaro"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon L\\\"uck's ultraproduct construction for team semantics and prove a suitable version of {\\L}o\\'s' Theorem. Second, we show that by working with suitably saturated models, we can generalize the proof of Kontinen and Yang to sets of formulas with arbitrarily many variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-07T14:45:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B60",
      "03C20",
      "03C85"
    ],
    "keywords": [
      "team semantics",
      "compactness theorem",
      "ultraproduct construction",
      "first-order logic",
      "suitably saturated models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}