{
  "id": "1609.05433",
  "version": "v1",
  "published": "2016-09-18T06:54:36.000Z",
  "updated": "2016-09-18T06:54:36.000Z",
  "title": "Coherent systems of finite support iterations",
  "authors": [
    "Vera Fischer",
    "Sy D. Friedman",
    "Diego A. Mejía",
    "Diana C. Montoya"
  ],
  "comment": "27 pages, 3 figures. Submitted",
  "categories": [
    "math.LO"
  ],
  "abstract": "We introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations in Cicho\\'n's diagram, in particular, a model where the diagram can be separated into 7 different values. Furthermore, we show that this constellation of 7 values is consistent with the existence of a $\\Delta^1_3$ well-order of the reals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-18T06:54:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E17",
      "03E15",
      "03E35",
      "03E40",
      "03E45"
    ],
    "keywords": [
      "finite support iterations",
      "construct three-dimensional arrays",
      "generic extensions",
      "constellation",
      "ccc posets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}