{
  "id": "2109.10618",
  "version": "v1",
  "published": "2021-09-22T09:33:43.000Z",
  "updated": "2021-09-22T09:33:43.000Z",
  "title": "Non-stationary support iterations of Prikry Forcings and Restrictions of Ultrapower Embeddings to the Ground Model",
  "authors": [
    "Moti Gitik",
    "Eyal Kaplan"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We study the nonstationary-support iteration of Prikry forcings below a measurable cardinal \\kappa, characterizing all the normal measures it carries in the generic extension. We then analyze the restriction of ultrapower embeddings, taken with such a normal measure in the generic extension, to the ground model. We prove that every such restriction is an iterated ultrapwer of the ground model, and provide a sufficient condition for its definability there. This is done without core-model theoretic arguments: the assumption that GCH holds in the ground model up to \\kappa suffices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-22T09:33:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ground model",
      "non-stationary support iterations",
      "ultrapower embeddings",
      "prikry forcings",
      "restriction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}