{
  "id": "2010.03664",
  "version": "v1",
  "published": "2020-10-07T21:33:17.000Z",
  "updated": "2020-10-07T21:33:17.000Z",
  "title": "Flow: the Axiom of Choice is independent from the Partition Principle",
  "authors": [
    "Adonai S. Sant'Anna",
    "Otavio Bueno",
    "Marcio P. P. de França",
    "Renato Brodzinski"
  ],
  "comment": "37 pages, 4 Figures",
  "categories": [
    "math.LO"
  ],
  "abstract": "We introduce a general theory of functions called Flow. We prove ZF, non-well founded ZF and ZFC can be immersed within Flow as a natural consequence from our framework. The existence of strongly inaccessible cardinals is entailed from our axioms. And our first important application is the introduction of a model of Zermelo-Fraenkel set theory where the Partition Principle (PP) holds but not the Axiom of Choice (AC). So, Flow allows us to answer to the oldest open problem in set theory: if PP entails AC.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-07T21:33:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partition principle",
      "independent",
      "oldest open problem",
      "zermelo-fraenkel set theory",
      "first important application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}