{
  "annotation_id": "0a08b4f6-b30d-4902-9606-b098f42fcbc7",
  "date_created": "2026-02-17T05:53:23.617000Z",
  "date_modified": "2026-02-17T05:53:23.617000Z",
  "file_hash": "5ffe773e13b3ee09c9a02b9aef57fcfb18c7d7eb0ba578887bcc4ede3451fbf6",
  "private": false,
  "record": {
    "abstract": "A proof will be presented that the existence of a non-trivial $\\Sigma_1$-elementary embedding $j: V_{\\lambda+3} \\prec V_{\\lambda+3}$ is inconsistent with $\\textsf{ZF}$. Sections 1 and 2 shall review various important contributions from the literature, notably including \\cite{Goldberg2020}, \\cite{Schlutzenberg2020}, and \\cite{Woodin2010}, the latter reference being where the crucial forcing construction is presented. Section 3 shall introduce some new large cardinal properties, of consistency strength intermediate between $\\mathsf{I_3}$ and $\\mathsf{I_2}$, and greater than $\\mathsf{I_1}$, respectively. The proof of the inconsistency with $\\mathsf{ZF}$ of the existence of a non-trivial $\\Sigma_1$-elementary embedding $j:V_{\\lambda+3} \\prec V_{\\lambda+3}$ shall be given in Section 4. The claims of Sections 2 and 4 are provable in $\\textsf{ZF}$; those of Section 3, with the exception of the last two theorems, in $\\textsf{ZFC}$.",
    "arxiv_id": "2601.10231",
    "authors": [
      "Rupert McCallum"
    ],
    "categories": [
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Inconsistency of Reinhardt cardinals with $\\mathsf{ZF}$",
    "url": "https://arxiv.org/abs/2601.10231",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "58bf0e1a-b6d1-4153-8de5-970437b645db",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}