{
  "id": "1906.02873",
  "version": "v1",
  "published": "2019-06-07T02:58:56.000Z",
  "updated": "2019-06-07T02:58:56.000Z",
  "title": "Initial self-embeddings of models of set theory",
  "authors": [
    "Ali Enayat",
    "Zachiri McKenzie"
  ],
  "comment": "29 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "By a classical theorem of Harvey Friedman (1973), every countable nonstandard model $\\mathcal{M}$ of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding $j$, i.e., $j$ is a self-embedding of $\\mathcal{M}$ such that $j[\\mathcal{M}]\\subsetneq\\mathcal{M}$, and the ordinal rank of each member of $j[\\mathcal{M}]$ is less than the ordinal rank of each element of $\\mathcal{M}\\setminus j[\\mathcal{M}]$. Here we investigate the larger family of proper initial-embeddings $j$ of models $\\mathcal{M}$ of fragments of set theory, where the image of $j$ is a transitive submodel of $\\mathcal{M}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-07T02:58:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F30"
    ],
    "keywords": [
      "set theory",
      "initial self-embeddings",
      "ordinal rank",
      "harvey friedman",
      "proper initial-embeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}