{
  "id": "1908.04477",
  "version": "v1",
  "published": "2019-08-13T04:07:11.000Z",
  "updated": "2019-08-13T04:07:11.000Z",
  "title": "Polarized relations at singulars over successors",
  "authors": [
    "Shimon Garti"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Erdos, Hajnal and Rado asked whether $\\binom{\\aleph_{\\omega_1}}{\\aleph_2}\\rightarrow\\binom{\\aleph_{\\omega_1}}{\\aleph_0}_2$ and whether $\\binom{\\aleph_{\\omega_1}}{\\aleph_2}\\rightarrow\\binom{\\aleph_{\\omega_1}}{\\aleph_1}_2$. We prove that both relations are independent over ZFC. We shall also prove that $\\binom{\\mu}{\\aleph_2}\\rightarrow\\binom{\\mu}{\\aleph_2}_2$ is independent over ZF for some $\\mu$ of cofinality $\\omega_1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-13T04:07:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E02",
      "03E25",
      "03E60"
    ],
    "keywords": [
      "polarized relations",
      "successors",
      "independent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}