{
  "id": "2401.00457",
  "version": "v1",
  "published": "2023-12-31T11:18:59.000Z",
  "updated": "2023-12-31T11:18:59.000Z",
  "title": "Filtrations for $\\mathbb{wK4}$ and its relatives",
  "authors": [
    "Andrey Kudinov",
    "Ilya Shapirovsky"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We study the finite model property of subframe logics with expressible transitive closure modality. For $m>0$, let $\\mathrm{L}_m$ be the logic given by axiom $\\lozenge^{m+1} p\\to \\lozenge p\\vee p$. We construct filtrations for the logics $\\mathrm{L}_m$. It follows that these logics and their tense counterparts have the finite model property. Then we show that every canonical subframe logic that contains $\\mathrm{L}_m$ have the finite model property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-31T11:18:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B45"
    ],
    "keywords": [
      "finite model property",
      "construct filtrations",
      "tense counterparts",
      "canonical subframe logic",
      "expressible transitive closure modality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}