nLab
extendible cardinal

Idea

An extendible cardinal is a type of large cardinal.

Definition

Definition

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

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