{
  "id": "0705.3803",
  "version": "v2",
  "published": "2007-05-25T19:25:26.000Z",
  "updated": "2007-05-25T20:15:35.000Z",
  "title": "On implications in sectionally pseudocomplemented posets",
  "authors": [
    "J\\{=}anis Cīrulis"
  ],
  "comment": "10 pages, no figures, typos corrected",
  "journal": "Acta Sci. Math. (Szeged) 74 (2008), 477--491",
  "categories": [
    "math.LO"
  ],
  "abstract": "A sectionally pseudocomplemented poset P is one which has the top element and in which every principal order filter is a pseudocomplemented poset. The sectional pseudocomplements give rise to an implication-like operation on P which coincides with the relative pseudocomplementation if P is relatively psudocomplemented. We characterise this operation and study some elementary properties of upper semilattices, lower semilattices and lattices equipped with this kind of implication. We deal also with a few weaker versions of implication. Sectionally pseudocomplemented lattices have already been studied in the literature.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-05-25T20:15:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03G25",
      "06A12",
      "06D15",
      "06F35"
    ],
    "keywords": [
      "sectionally pseudocomplemented poset",
      "implication",
      "principal order filter",
      "sectional pseudocomplements",
      "weaker versions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.3803C"
    }
  }
}