{
  "id": "1602.07901",
  "version": "v1",
  "published": "2016-02-25T12:22:37.000Z",
  "updated": "2016-02-25T12:22:37.000Z",
  "title": "Suslin trees, the bounding number, and partition relations",
  "authors": [
    "Dilip Raghavan",
    "Stevo Todorcevic"
  ],
  "comment": "17 pages, submitted",
  "categories": [
    "math.LO"
  ],
  "abstract": "We investigate the unbalanced ordinary partition relations of the form $\\lambda \\rightarrow {(\\lambda, \\alpha)}^{2}$ for various values of the cardinal $\\lambda$ and the ordinal $\\alpha$. For example, we show that for every infinite cardinal $\\kappa,$ the existence of a ${\\kappa}^{+}-$Suslin tree implies ${\\kappa}^{+} \\not\\rightarrow {\\left( {\\kappa}^{+}, {\\log}_{\\kappa}({\\kappa}^{+}) + 2 \\right)}^{2}$. The consistency of the positive partition relation $\\mathfrak{b} \\rightarrow {(\\mathfrak{b}, \\alpha)}^{2}$ for all $\\alpha < {\\omega}_{1}$ for the bounding number $\\mathfrak{b}$ is also established from large cardinals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-25T12:22:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E02",
      "03E17",
      "03E55",
      "03E50"
    ],
    "keywords": [
      "bounding number",
      "unbalanced ordinary partition relations",
      "suslin tree implies",
      "large cardinals",
      "positive partition relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160207901R"
    }
  }
}