{
  "id": "1906.09307",
  "version": "v1",
  "published": "2019-06-21T20:06:50.000Z",
  "updated": "2019-06-21T20:06:50.000Z",
  "title": "Representability and Compactness for Pseudopowers",
  "authors": [
    "Todd Eisworth"
  ],
  "comment": "Pre-submission version",
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove a compactness theorem for pseudopower operations of the form $pp_{\\Gamma(\\mu,\\sigma)}(\\mu)$ where $\\aleph_0<\\sigma=cf(\\sigma)\\leq cf(\\mu)$. Our main tool is a result that has Shelah's cov vs. pp Theorem as a consequence. We also show that the failure of compactness in other situations has significant consequences for pcf theory, in particular, implying the existence of a progressive set $A$ of regular cardinals for which $pcf(A)$ has an inaccessible accumulation point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-21T20:06:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E04"
    ],
    "keywords": [
      "representability",
      "pseudopower operations",
      "main tool",
      "shelahs cov",
      "compactness theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}