{
  "id": "2308.01072",
  "version": "v1",
  "published": "2023-08-02T10:47:57.000Z",
  "updated": "2023-08-02T10:47:57.000Z",
  "title": "Local Definability of $\\mathsf{HOD}$ in $L(\\mathbb{R})$",
  "authors": [
    "Obrad Kasum"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that in $L(\\mathbb{R})$, assuming large cardinals, $\\mathsf{HOD} {\\parallel}\\eta^{+\\mathsf{HOD}}$ is locally definable from $\\mathsf{HOD} {\\parallel}\\eta$ for all $\\mathsf{HOD}$-cardinals $\\eta\\in [\\boldsymbol{\\delta}^2_1,\\Theta)$. This is a further elaboration of the statement \"$\\mathsf{HOD}^{L(\\mathbb{R})}$ is a core model below $\\Theta$\" made by John Steel.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-02T10:47:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E45"
    ],
    "keywords": [
      "local definability",
      "core model",
      "assuming large cardinals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}