Definition:Strongly Inaccessible Cardinal

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


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