# Extendible cardinals

## Idea

An extendible cardinal is a type of large cardinal.

## Definition

###### Definition

If $\kappa\lt\lambda$, we say $\kappa$ is $\lambda$-extendible if there is an elementary embedding $j:V_\lambda \to V_\mu$ with critical point $\kappa$ such that $j(\kappa)\gt \lambda$.

We say $\kappa$ is extendible if it is $\lambda$-extendible for all $\lambda\gt\kappa$.

Created on September 24, 2012 06:17:31 by Mike Shulman (192.16.204.218)