Definition:Strongly Inaccessible Cardinal

Definition

An infinite cardinal $\aleph_\kappa$ is called a strongly inaccessible cardinal if and only if:

$(1): \quad \aleph_\kappa$ is a weakly inaccessible cardinal

$(2): \quad \forall x \in \kappa: \card {\powerset x} \in \kappa$

Sources

• 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 10.66 \ (2)$