{
  "annotation_id": "02ff7110-a0ac-4c93-a22d-29f3051cbcd6",
  "date_created": "2026-02-17T05:53:16.290000Z",
  "date_modified": "2026-02-17T05:53:16.290000Z",
  "file_hash": "76b586e91cb84e114451c98a8fbab50dea6727d910c6b8f6ef12ca5ff6e4559a",
  "private": false,
  "record": {
    "abstract": "We show Shelah\u0027s original creature forcing from 1984 strongly preserves tight mad families. In particular, answering questions of Fischer and Friedman and Friedman and Zdomskyy, we show the constellation $\\aleph_1 = \\mathfrak{a} \u003c \\mathfrak{s} = \\aleph_2$ is consistent with the existence of a $\\Delta_3^1$ wellorder of the reals and tight mad families of sizes $\\aleph_1, \\aleph_2$ which are $\\Pi_1^1, \\Pi_2^1$-definable, respectively. Each of these projective definitions is of minimal possible complexity.",
    "arxiv_id": "2601.08718",
    "authors": [
      "Vera Fischer",
      "Julia Millhouse"
    ],
    "categories": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Strong Projective Witnesses",
    "url": "https://arxiv.org/abs/2601.08718",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6d00620e-a787-4eb7-a689-f3325fcc3a52",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}