---
tag: KZ7KDKXYEQ
kind: concept
name: Shelah cardinal
sources:
  - wikipedia: en:529392@r1211749340
    locator: Shelah cardinal
    note: adopted
    mention: wikipedia://en/529392
    sections: [Summary]
same_as:
  wikidata: Q7493307
  wikipedia: Shelah cardinal
inventory: [6DQVEX2EZK]
---

## Summary

In 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 $V_{j(f)(\kappa )}\subset N$.