{
  "id": "math/0403186",
  "version": "v1",
  "published": "2004-03-10T21:23:50.000Z",
  "updated": "2004-03-10T21:23:50.000Z",
  "title": "Unified Foundations for Mathematics",
  "authors": [
    "Mark Burgin"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole mathematics. Set theory has been for a long time the most popular foundation. However, it was not been able to win completely over its rivals: logic, the theory of algorithms, and theory of categories. Moreover, practical applications of mathematics and its inner problems caused creation of different generalization of sets: multisets, fuzzy sets, rough sets etc. Thus, we encounter a problem: Is it possible to find the most fundamental structure in mathematics? The situation is similar to the quest of physics for the most fundamental \"brick\" of nature and for a grand unified theory of nature. It is demonstrated that in contrast to physics, which is still in search for a unified theory, in mathematics such a theory exists. It is the theory of named sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-03-10T21:23:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B30"
    ],
    "keywords": [
      "mathematics",
      "unified foundations",
      "inner problems",
      "set theory",
      "fundamental structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}