{
  "annotation_id": "4bf52174-4c05-4845-a01a-816623a1c3be",
  "date_created": "2026-02-17T05:53:11.892000Z",
  "date_modified": "2026-02-17T05:53:11.892000Z",
  "file_hash": "57155d8b2032e0ae7822a2248f85bc229ad1a057a3f7156684b206727aadad54",
  "private": false,
  "record": {
    "abstract": "We construct an $\\ll^2$-solution (also known as a weakly low solution) to ${\\mathrm{D}^2}$ within ${\\mathrm{B}\\Sigma^0_{3}}$ and prove the $\\ll^2$-basis theorem for $\\mathrm{RT}^2$ over ${\\mathrm{B}\\Sigma^0_{3}}$. The $\\ll^2$-basis theorem is a variant of the low basis theorem, which has recently received focus in the context of the first-order part of Ramsey type theorems. For the construction, we use Mathias forcing in an effectively coded $\\omega$-model of $\\mathsf{WKL_0}$ to ensure sufficient computability under the system with weaker induction. Using a similar method, we also show the $\\ll^2$-basis theorem for $\\mathrm{RT}^2_2$ and $\\mathrm{EM}_{\u003c\\infty}$, a version of Erd\\H{o}s-Moser principle, within $\\mathrm{I}\\Sigma^0_{2}$. These results provide simpler proofs of known results on the $\\Pi^1_1$-conservativities of $\\mathrm{RT}^2, \\mathrm{RT}^2_2$ and $\\mathrm{EM}_{\u003c\\infty}$ as corollaries.",
    "arxiv_id": "2601.07569",
    "authors": [
      "Hiroyuki Ikari",
      "Keita Yokoyama"
    ],
    "categories": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Low-like basis theorems for Ramsey\u0027s theorem for pairs in first-order arithmetic",
    "url": "https://arxiv.org/abs/2601.07569",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "55c8e978-558f-447f-8bdf-0bf90f9d2216",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}