{
  "id": "0812.3489",
  "version": "v2",
  "published": "2008-12-18T10:10:27.000Z",
  "updated": "2009-05-31T03:38:06.000Z",
  "title": "Krull dimension of types in a class of first-order theories",
  "authors": [
    "Domenico Zambella"
  ],
  "comment": "Major revision, new title",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula--plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-companion is strongly minimal. We also prove that the length of any increasing sequence of prime types is bounded, so every formula has finite Krull dimension.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-31T03:38:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60"
    ],
    "keywords": [
      "first-order theories",
      "finite krull dimension",
      "complete quantifier-free types",
      "theory fields",
      "prime types"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.3489Z"
    }
  }
}