Main Page | See live article | Alphabetical index In mathematics, 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 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. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.