{
  "id": "1811.08457",
  "version": "v2",
  "published": "2018-11-20T19:35:32.000Z",
  "updated": "2019-12-07T12:33:47.000Z",
  "title": "Monochromatic Sumset Without the use of large cardinals",
  "authors": [
    "Jing Zhang"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We show in this note that in the forcing extension by $Add(\\omega,\\beth_{\\omega})$, the following Ramsey property holds: for any $r\\in \\omega$ and any $f: \\mathbb{R}\\to r$, there exists an infinite $X\\subset \\mathbb{R}$ such that $X+X$ is monochromatic under $f$. We also show the Ramsey statement above is true in $\\mathrm{ZFC}$ when $r=2$. This answers two questions by Komj\\'ath, Leader, Russell, Shelah, Soukup and Vidny\\'anszky.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-12-07T12:33:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large cardinals",
      "monochromatic sumset",
      "ramsey property holds",
      "ramsey statement",
      "forcing extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}