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
$(2): \quad \forall x \in \kappa: \left|{\mathcal P \left({x}\right)}\right| \in \kappa$


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