Definition:Strongly Inaccessible Cardinal
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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: $\S 10.66 \ (2)$