{
  "id": "1805.11342",
  "version": "v1",
  "published": "2018-05-29T10:14:20.000Z",
  "updated": "2018-05-29T10:14:20.000Z",
  "title": "Splittings and disjunctions in Reverse Mathematics",
  "authors": [
    "Sam Sanders"
  ],
  "comment": "12 pages, one table",
  "categories": [
    "math.LO"
  ],
  "abstract": "Reverse Mathematics (RM hereafter) is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the minimal axioms needed to prove a theorem of ordinary, i.e. non-set-theoretic, mathematics. As suggested by the title, this paper deals with two (relatively rare) RM-phenomena, namely splittings and disjunctions. As to splittings, there are some examples in RM of theorems $A, B, C$ such that $A\\leftrightarrow (B\\wedge C)$, i.e. $A$ can be split into two independent (fairly natural) parts $B$ and $C$. As to disjunctions, there are (very few) examples in RM of theorems $D, E, F$ such that $D\\leftrightarrow (E\\vee F)$, i.e. $D$ can be written as the disjunction of two independent (fairly natural) parts $E$ and $F$. By contrast, we show in this paper that there is a plethora of (natural) splittings and disjunctions in Kohlenbach's higher-order RM.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-29T10:14:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B30",
      "03F35"
    ],
    "keywords": [
      "reverse mathematics",
      "disjunction",
      "splittings",
      "kohlenbachs higher-order rm",
      "fairly natural"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}