{
  "id": "2309.00392",
  "version": "v1",
  "published": "2023-09-01T11:10:29.000Z",
  "updated": "2023-09-01T11:10:29.000Z",
  "title": "A decidable expansion of $(Γ,+,F)$ with the independence property",
  "authors": [
    "Françoise Point"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let $(\\Gamma,+,F)$ be a finitely generated $\\mathbb Z[F]$-module where $F$ is an injective endomorphism of the abelian group $\\Gamma$. We restrict ourselves to a finite automa presentable subclass, introduced by J. Bell and R. Moosa in \"F-sets and finite automata. J. Th\\'eor. Nombres Bordeaux 31 (2019), no. 1, 101-130\" and define an expansion containing the $\\mathcal F$-sets defined by R. Moosa and T. Scanlon in \"Am. J. Math. 126 (2004), no. 3, p. 473-522\", where every automatic subset is definable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-01T11:10:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "11B85",
      "68Q45"
    ],
    "keywords": [
      "independence property",
      "decidable expansion",
      "finite automa presentable subclass",
      "nombres bordeaux",
      "finite automata"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}