{
  "id": "1509.07377",
  "version": "v1",
  "published": "2015-09-24T14:00:19.000Z",
  "updated": "2015-09-24T14:00:19.000Z",
  "title": "$μ$-Abstract Elementary Classes and other generalizations",
  "authors": [
    "Will Boney",
    "Rami Grossberg",
    "Michael Lieberman",
    "Jiri Rosicky",
    "Sebastien Vasey"
  ],
  "comment": "24 pp",
  "categories": [
    "math.LO",
    "math.CT"
  ],
  "abstract": "We introduce $\\mu$-Abstract Elementary Classes ($\\mu$-AECs) as a broad framework for model theory that includes complete boolean algebras and Dirichlet series, and begin to develop their classification theory. Moreover, we note that $\\mu$-AECs correspond precisely to accessible categories in which all morphisms are monomorphisms, and begin the process of reconciling these divergent perspectives: not least, the preliminary classification-theoretic results for {\\mu}-AECs transfer directly to accessible categories with monomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-24T14:00:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C48",
      "03C45",
      "18C35",
      "03C52",
      "03C55",
      "03C75",
      "03E55"
    ],
    "keywords": [
      "abstract elementary classes",
      "generalizations",
      "complete boolean algebras",
      "accessible categories",
      "preliminary classification-theoretic results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150907377B"
    }
  }
}