Definition:Strongly Inaccessible Cardinal

Definition
An infinite cardinal $\aleph_\kappa$ is called strongly inaccessible cardinal iff:


 * $(1): \quad \aleph_\kappa$ is a weakly inaccessible cardinal.
 * $(2): \quad \forall x \in \kappa: \left|{ \mathcal P \left({ x }\right) }\right| \in \kappa$