Strongly inaccessible cardinal
, a cardinal number
κ > א0
is called strongly inaccessible iff
the following conditions hold:
- κ is regular; that is, cf(κ) = κ.
- κ is a strong limit cardinal, that is, 2λ < κ for all λ < κ.
Assuming that ZFC
, 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.