{
  "id": "2409.09697",
  "version": "v1",
  "published": "2024-09-15T11:16:02.000Z",
  "updated": "2024-09-15T11:16:02.000Z",
  "title": "Adding Abraham clubs and $α$-properness",
  "authors": [
    "Mohammad Golshani",
    "Rouholah Hoseini Naveh"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "For every indecomposable ordinal $\\alpha < \\omega_1$, we introduce a variant of Abraham forcing for adding a club in $\\omega_1$, which is $<\\alpha$-proper but not $\\alpha$-proper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-15T11:16:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adding abraham clubs",
      "properness",
      "indecomposable ordinal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}