strongly inaccessible cardinal

In mathematics, a strongly inaccessible cardinal is an uncountable cardinal number κ that is regular and a strong limit cardinal. In other words

the cofinality cf(κ) = κ, and
2^λ < κ for all λ < κ.

Assuming that ZFC is consistent, the existence of strongly inaccessible cardinals provably cannot be proved in ZFC. Strongly inaccessible cardinals are therefore a type of large cardinal. Under the Generalized Continuum Hypothesis, a cardinal is strongly inaccessible if and only if it is weakly inaccessible. The assumption of the existence of a strongly inaccessible cardinal is sometimes applied in the form of the assumption that one can work inside a Grothendieck universe, the two ideas being intimately connected

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