{
  "abstract": "Hayut and the first author isolated the notion of a critical cardinal in [1]. In this work, we answer several questions raised in the original paper. We show that it is consistent for a critical cardinal not to have any ultrapower elementary embeddings, as well as that it is consistent that no target model is closed. We also prove that if κ κ is a critical point by any ultrapower embedding, then it is the critical point of an ultrapower embedding by a normal measure. The paper concludes by presenting several open questions of interest in the study of critical cardinals.",
  "abstract_shown": true,
  "affiliations": [
    "School of Mathematics, University of Leeds, Leeds, LS2 9JT UK"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Asaf Karagila",
      "orcid": "0000-0003-1289-0904"
    },
    {
      "affs": [
        0
      ],
      "name": "Jiachen Yuan",
      "orcid": "0009-0000-3435-0840"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/737cp14hwdmwk.bib",
  "cited_by": 0,
  "doi": "10.1007/s00605-026-02215-0",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13736446/",
  "id": "737cp14hwdmwk",
  "issns": [
    "0026-9255",
    "1436-5081"
  ],
  "landing_url": "https://doi.org/10.1007/s00605-026-02215-0",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Article"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W4390690475",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s00605-026-02215-0.pdf",
  "pmcid": "PMC13736446",
  "pmid": "42991611",
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/737cp14hwdmwk.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:53Z",
      "native_id": "PMC13736446",
      "source": "pmc",
      "url": "https://doi.org/10.1007/s00605-026-02215-0"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Advanced Topology and Set Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Critical embeddings",
  "title_text": "Critical embeddings",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T12:21:53Z",
  "url": "https://research.draconitic.com/paper/737cp14hwdmwk",
  "venue": "Monatshefte Fur Mathematik",
  "versions": []
}