{
  "id": "1805.04834",
  "version": "v1",
  "published": "2018-05-13T07:11:31.000Z",
  "updated": "2018-05-13T07:11:31.000Z",
  "title": "Approximations of Mappings",
  "authors": [
    "Jaroslav Nesetril",
    "Patrice Ossona de Mendez"
  ],
  "categories": [
    "math.CO",
    "math.LO"
  ],
  "abstract": "We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem of the construction of a continuous limit for first-order convergent sequences of finite mappings. We solve the approximation problem and, consequently, the full characterization of limit objects for mappings for first-order (i.e. ${\\rm FO}$) convergence and local (i.e. ${\\rm FO}^{\\rm local}$) convergence. This work can be seen both as a first step in the resolution of inverse problems (like Aldous-Lyons conjecture) and a strengthening of the classical decidability result for finite satisfiability in Rabin class (which consists of first-order logic with equality, one unary function, and an arbitrary number of monadic predicates). The proof involves model theory and analytic techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-13T07:11:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse problem",
      "first-order convergent sequences",
      "finite mapping",
      "unary relations",
      "analytic techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}