{
  "id": "2307.06846",
  "version": "v1",
  "published": "2023-07-13T16:08:22.000Z",
  "updated": "2023-07-13T16:08:22.000Z",
  "title": "A note on the incompleteness of Afshari & Leigh's system Clo",
  "authors": [
    "Johannes Kloibhofer"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "The system $\\mathsf{Clo}$ is a cyclic, cut-free proof system for the modal $\\mu$-calculus. It was introduced by Afshari & Leigh as an intermediate system in their intent to show the completeness of Kozen's axiomatisation for the modal $\\mu$-calculus. We prove that $\\mathsf{Clo}$ is incomplete by giving a valid sequent that is not provable in $\\mathsf{Clo}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-13T16:08:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "leighs system clo",
      "incompleteness",
      "cut-free proof system",
      "intermediate system",
      "valid sequent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}