Strongly inaccessible cardinal

In mathematics, a cardinal number κ > ‭א‬₀ is called strongly inaccessible iff the following conditions hold:

1. κ is regular; that is, cf(κ) = κ.
2. κ is a strong limit cardinal, that is, 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 iff it is weakly inaccessible.