{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn axiomatic set theory, **Shelah cardinals** are a kind of large cardinals. A [[cardinal|0EBACQFAZW]] $\\kappa$ is called Shelah iff for every $f:\\kappa\\rightarrow\\kappa$, there exists a transitive class $N$ and an elementary embedding $j:V\\rightarrow N$ with critical point $\\kappa$; and $V_{j(f)(\\kappa )}\\subset N$.\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "inventory": [
      "6DQVEX2EZK"
    ],
    "kind": "concept",
    "name": "Shelah cardinal",
    "same_as": {
      "wikidata": "Q7493307",
      "wikipedia": "Shelah cardinal"
    },
    "sources": [
      {
        "locator": "Shelah cardinal",
        "mention": "wikipedia://en/529392",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:529392@r1211749340"
      }
    ],
    "tag": "KZ7KDKXYEQ"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/KZ7KDKXYEQ/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/KZ7KDKXYEQ.md",
  "msc": null,
  "name": "Shelah cardinal",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/KZ7/KZ7KDKXYEQ.md",
  "status": null,
  "tag": "KZ7KDKXYEQ",
  "uri": "m2://KZ7KDKXYEQ",
  "url": "https://math2.tamnd.com/wiki/shelah-cardinal/",
  "writing": {
    "tag": "KZ7KDKXYEQ",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}