Strongly inaccessible cardinal
A cardinal number κ > א0 is called strongly inaccessible iff the following conditions hold: κ is weakly inaccessible; that is, cf(κ) = κ. κ is a strong limit[?], that is, 2λ < κ for all λ < κ. Assuming that ZFC is consistent, the existence of strongly inaccessible cardinals provably cannot be proved in ZFC.
Assuming that ZFC is consistent, the existence of strongly inaccessible cardinals provably cannot be proved in ZFC.