{
  "id": "2009.01127",
  "version": "v1",
  "published": "2020-09-02T15:06:21.000Z",
  "updated": "2020-09-02T15:06:21.000Z",
  "title": "Taking Reinhardt's Power Away",
  "authors": [
    "Richard Matthews"
  ],
  "comment": "25 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study the notion of non-trivial elementary embeddings $j : V \\rightarrow V$ under the assumption that $V$ satisfies $ZFC$ without Power Set but with the Collection Scheme. We show that no such embedding can exist under the additional assumption that it is cofinal and either $V_{\\textrm{crit}(j)}$ is a set or that the Reflection Principle holds. We then study failures of instances of collection in symmetric submodels of both set and class forcings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-02T15:06:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E55",
      "03E30",
      "03E25"
    ],
    "keywords": [
      "reinhardts power away",
      "non-trivial elementary embeddings",
      "reflection principle holds",
      "additional assumption",
      "collection scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}