{
  "id": "2410.23967",
  "version": "v1",
  "published": "2024-10-31T14:21:19.000Z",
  "updated": "2024-10-31T14:21:19.000Z",
  "title": "$Σ_1$-Stationary logic as an $\\aleph_1$-Abstract Elementary Class",
  "authors": [
    "Will Boney"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "$\\mu$-Abstract Elementary Classes are a model theoretic framework introduced in [BGL+16] to encompass classes axiomatized by $\\mathbb{L}_{\\infty, \\infty}$. We show that the framework extends beyond these logics by showing classes axiomatized in $\\mathbb{L}(aa)$ with just the $aa$ quantifier are an $\\aleph_1$-Abstract Elementary Class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-31T14:21:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abstract elementary class",
      "stationary logic",
      "model theoretic framework",
      "framework extends",
      "encompass classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}