{
  "id": "0709.2979",
  "version": "v2",
  "published": "2007-09-19T10:17:59.000Z",
  "updated": "2007-09-19T20:22:07.000Z",
  "title": "Choice and Regularity: Common Consequences in Logic",
  "authors": [
    "Denis I. Saveliev"
  ],
  "comment": "37 pages, slides of a talk at the 2nd World Congress on Universal Logic (20-22 August 2007, Xi'an). All these results were obtained about 2004 and announced at seminars of Moscow State University, Department of Mechanics and Mathematics",
  "categories": [
    "math.LO"
  ],
  "abstract": "It is well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating their \"intersection\", a principle (called here Best-Foundedness) which is consistent with the negations of both axioms but implies all these consequences. Then we study relationships between these consequences (and near principles) in detail. Finally, we consider some arguments related to truth of various principles in set theory, especially arguments concerning the interpretability strength.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-09-19T20:22:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E30",
      "03E35",
      "03E45",
      "03E55",
      "03E65"
    ],
    "keywords": [
      "regularity",
      "important common consequences",
      "interpretability strength",
      "study relationships",
      "set theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2979S"
    }
  }
}