{
  "id": "1812.01264",
  "version": "v1",
  "published": "2018-12-04T08:04:38.000Z",
  "updated": "2018-12-04T08:04:38.000Z",
  "title": "Definable operators on stable set lattices",
  "authors": [
    "Robert Goldblatt"
  ],
  "comment": "18 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Structures based on polarities provide relational semantics for non-distributive logics. Such structures have associated complete lattices of stable subsets, and these have been used to construct canonical extensions of lattice-based algebras. We study classes of structures that are closed under ultraproducts and whose stable set lattices have additional operators that are first-order definable in the underlying structure. We show that such classes generate varieties of algebras that are closed under canonical extensions. This lifts a fundamental result from modal model theory to the non-distributive level. The proof makes use of a relationship between canonical extensions and MacNeille completions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-04T08:04:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03G10",
      "06B23",
      "03C20",
      "06A15",
      "06D50"
    ],
    "keywords": [
      "stable set lattices",
      "definable operators",
      "modal model theory",
      "classes generate varieties",
      "fundamental result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}