{
  "id": "2012.04004",
  "version": "v1",
  "published": "2020-12-07T19:16:34.000Z",
  "updated": "2020-12-07T19:16:34.000Z",
  "title": "Uniform Birkhoff",
  "authors": [
    "Mai Gehrke",
    "Michael Pinsker"
  ],
  "comment": "10 pages. (This material contains old results from 2014 published in 2018 (see reference), but so far not on arXiv)",
  "journal": "Journal of Pure And Applied Algebra, Volume 222, Issue 5, May 2018, Pages 1242-1250",
  "doi": "10.1016/j.jpaa.2017.06.016",
  "categories": [
    "math.LO",
    "math.RA"
  ],
  "abstract": "We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free algebra for $C$: the members of $C$ then are precisely those finitely generated algebras $A$ for which the natural mapping from the free algebra onto the term clone of $A$ is well-defined and uniformly continuous with respect to the uniformity $U$ and the uniformity of pointwise convergence on the term clone of $A$, respectively. Our result unifies earlier theorems describing pseudovarieties of finite algebras and the pseudovariety generated by a single oligomorphic algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-07T19:16:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniform birkhoff",
      "finitely generated algebras",
      "free algebra",
      "result unifies earlier theorems",
      "term clone"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}