{
  "id": "2106.13968",
  "version": "v1",
  "published": "2021-06-26T08:34:21.000Z",
  "updated": "2021-06-26T08:34:21.000Z",
  "title": "EMSO(FO$^2$) 0-1 law fails for all dense random graphs",
  "authors": [
    "Margarita Akhmejanova",
    "Maksim Zhukovskii"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we disprove EMSO(FO$^2$) convergence law for the binomial random graph $G(n,p)$ for any constant probability $p$. More specifically, we prove that there exists an existential monadic second order sentence with 2 first order variables such that, for every $p\\in(0,1)$, the probability that it is true on $G(n,p)$ does not converge.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-26T08:34:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dense random graphs",
      "law fails",
      "existential monadic second order sentence",
      "binomial random graph",
      "first order variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}