{
  "id": "1610.02191",
  "version": "v1",
  "published": "2016-10-07T08:53:58.000Z",
  "updated": "2016-10-07T08:53:58.000Z",
  "title": "Proof Theory of Constructive Systems: Inductive Types and Univalence",
  "authors": [
    "Michael Rathjen"
  ],
  "comment": "28 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "In Feferman's work, explicit mathematics and theories of generalized inductive definitions play a central role. One objective of this article is to describe the connections with Martin-Lof type theory and constructive Zermelo-Fraenkel set theory. Proof theory has contributed to a deeper grasp of the relationship between different frameworks for constructive mathematics. Some of the reductions are known only through ordinal-theoretic characterizations. The paper also addresses the strength of Voevodsky's univalence axiom. A further goal is to investigate the strength of intuitionistic theories of generalized inductive definitions in the framework of intuitionistic explicit mathematics that lie beyond the reach of Martin-Lof type theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-07T08:53:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F30",
      "03F50",
      "03C62"
    ],
    "keywords": [
      "proof theory",
      "constructive systems",
      "inductive types",
      "martin-lof type theory",
      "intuitionistic explicit mathematics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}