{
  "id": "2107.02577",
  "version": "v1",
  "published": "2021-07-06T12:34:08.000Z",
  "updated": "2021-07-06T12:34:08.000Z",
  "title": "Strong downward Löwenheim-Skolem theorems for stationary logics, III -- mixed support iteration",
  "authors": [
    "Sakaé Fuchino",
    "André Ottenbreit Maschio Rodrigue",
    "Hiroshi Sakai"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Continuing [Fuchino, Ottenbreit and Sakai[9, 10]] and [Fuchino and Ottenbreit[11]], we further study reflection principles in connection with the L\\\"owenheim-Skolem Theorems of stationary logics. In this paper, we mainly analyze the situations in the models obtained by mixed support iteration of a supercompact length and then collapsing another supercompact cardinal to make it $(2^{\\aleph_0})^+$. We show, among other things, that the reflection down to $< 2^{\\aleph_0}$ of the non-metrizability of topological spaces with small character is independent from the reflection properties studied in [Fuchino, Ottenbreit and Sakai[9, 10]] and [Fuchino and Ottenbreit[11]].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-06T12:34:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E55",
      "03E65",
      "03E75",
      "05C63",
      "54E35"
    ],
    "keywords": [
      "strong downward löwenheim-skolem theorems",
      "mixed support iteration",
      "stationary logics",
      "ottenbreit",
      "study reflection principles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}