{
  "id": "2301.01671",
  "version": "v1",
  "published": "2023-01-04T15:51:08.000Z",
  "updated": "2023-01-04T15:51:08.000Z",
  "title": "Sums of triples in Abelian groups",
  "authors": [
    "Ido Feldman",
    "Assaf Rinot"
  ],
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "abstract": "Motivated by a problem in additive Ramsey theory, we extend Todorcevic's partitions of three-dimensional combinatorial cubes to handle additional three-dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for every Abelian group $G$ of size $\\aleph_2$, there exists a coloring $c:G\\rightarrow\\mathbb Z$ such that for every uncountable $X\\subseteq G$ and every integer $k$, there are three distinct elements $x,y,z$ of $X$ such that $c(x+y+z)=k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-04T15:51:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E02",
      "03E75",
      "03E35",
      "05A17"
    ],
    "keywords": [
      "abelian group",
      "handle additional three-dimensional objects",
      "extend todorcevics partitions",
      "continuum hypothesis fails",
      "three-dimensional combinatorial cubes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}