{
  "id": "2211.13749",
  "version": "v1",
  "published": "2022-11-24T18:30:35.000Z",
  "updated": "2022-11-24T18:30:35.000Z",
  "title": "On projections of the tails of a power",
  "authors": [
    "Samuel M. Corson",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO",
    "math.GR",
    "math.RA"
  ],
  "abstract": "Let $\\kappa$ be an inaccessible cardinal, $\\mathfrak{U}$ be a universal algebra, and $\\sim$ be the equivalence relation on $\\mathfrak{U}^{\\kappa}$ of eventual equality. From mild assumptions on $\\kappa$ we give general constructions of $\\mathcal{E} \\in End(\\mathfrak{U}^{\\kappa}/\\sim)$ satisfying $\\mathcal{E} \\circ \\mathcal{E} = \\mathcal{E}$ which do not descend from $\\Delta \\in End(\\mathfrak{U}^{\\kappa})$ having small strong supports. As an application there exists an $\\mathcal{E} \\in End(\\mathbb{Z}^{\\kappa}/\\sim)$ which does not come from a $\\Delta \\in End(\\mathbb{Z}^{\\kappa})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-24T18:30:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20A15",
      "03E55",
      "03G05"
    ],
    "keywords": [
      "projections",
      "small strong supports",
      "equivalence relation",
      "eventual equality",
      "universal algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}