nLab
extendible cardinal

Extendible cardinals

Idea

An extendible cardinal is a type of large cardinal.

Definition

Definition

If κ<λ\kappa\lt\lambda, we say κ\kappa is λ\lambda-extendible if there is an elementary embedding j:V λV μj:V_\lambda \to V_\mu with critical point κ\kappa such that j(κ)>λj(\kappa)\gt \lambda.

We say κ\kappa is extendible if it is λ\lambda-extendible for all λ>κ\lambda\gt\kappa.

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