---
tag: WMS8APTDYF
kind: concept
name: Supercompact
sources:
  - wikipedia: en:43580500@r1360947732
    locator: Glossary of set theory, section S
    note: adopted
    mention: wikipedia://en/43580500#F25H
    sections: [Summary]
inventory: [YBK72J66AE]
---

## Summary

A supercompact cardinal is an uncountable cardinal *κ* such that for every *A* such that Card(*A*) ≥ *κ* there exists a normal measure over \[*A*\]<sup>*κ*</sup>.