{
  "id": "1610.05445",
  "version": "v1",
  "published": "2016-10-18T05:54:37.000Z",
  "updated": "2016-10-18T05:54:37.000Z",
  "title": "A weak variant of Hindman's Theorem stronger than Hilbert's Theorem",
  "authors": [
    "Lorenzo Carlucci"
  ],
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "abstract": "Hirst investigated a slight variant of Hindman's Finite Sums Theorem -- called Hilbert's Theorem -- and proved it equivalent over $\\RCA_0$ to the Infinite Pigeonhole Principle. This gave the first example of a finitistically reducible variant of Hindman's Theorem. We here introduce another natural variant of Hindman's Theorem -- which we name the Adjacent Hindman's Theorem -- and prove it to be strictly stronger than the Infinite Pigeonhole Principle and at most as strong as Ramsey's Theorem for colorings of pairs in $2$ colors (in the sense of Reverse Mathematics). In the Adjacent Hindman's Theorem homogeneity is required only for finite sums of adjacent elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-18T05:54:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hindmans theorem stronger",
      "hilberts theorem",
      "weak variant",
      "infinite pigeonhole principle",
      "hindmans finite sums theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}