{
  "id": "0807.3461",
  "version": "v2",
  "published": "2008-07-22T12:26:32.000Z",
  "updated": "2008-07-23T11:25:50.000Z",
  "title": "A simple proof that any additive basis has only finitely many essential subsets",
  "authors": [
    "Bakir Farhi"
  ],
  "comment": "3 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A$ be an additive basis. We call ``essential subset'' of $A$ any finite subset $P$ of $A$ such that $A \\setminus P$ is not an additive basis and that $P$ is minimal (for the inclusion order) to have this property. A recent theorem due to B. Deschamps and the author states that any additive basis has only finitely many essential subsets (see ``Essentialit\\'e dans les bases additives, J. Number Theory, 123 (2007), p. 170-192''). The aim of this note is to give a simple proof of this theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-07-23T11:25:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B13"
    ],
    "keywords": [
      "additive basis",
      "essential subset",
      "simple proof",
      "finite subset",
      "inclusion order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.3461F"
    }
  }
}