{
  "id": "math/0105136",
  "version": "v1",
  "published": "2001-05-16T17:06:53.000Z",
  "updated": "2001-05-16T17:06:53.000Z",
  "title": "Model Companions of T_σfor stable T",
  "authors": [
    "John Baldwin",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let T be a complete first order theory in a countable relational language L . We assume relation symbols have been added to make each formula equivalent to a predicate. Adjoin a new unary function symbol sigma to obtain the language L_sigma; T_sigma is obtained by adding axioms asserting that sigma is an L-automorphism. We provide necessary and sufficient conditions for T_sigma to have a model companion when T is stable. Namely, we introduce a new condition: T_sigma admits obstructions, and show that T_sigma has a model companion iff and only if T_sigma does not admit obstructions. This condition is weakening of the finite cover property: if a stable theory T has the finite cover property then T_sigma admits obstructions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-05-16T17:06:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "model companion",
      "finite cover property",
      "complete first order theory",
      "admits obstructions",
      "unary function symbol sigma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......5136B"
    }
  }
}