Encyclopedia > Strongly inaccessible cardinal

Article Content

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, 2^λ < κ for all λ < κ.

Assuming that ZFC is consistent, the existence of strongly inaccessible cardinals provably cannot be proved in ZFC.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia

Search over one million articles, find something about almost anything!

Featured Article

Springs, New York

... the median income for a family is $66,607. Males have a median income of $42,500 versus $32,107 for females. The per capita income for the town is $29,910. 8.7% of the ...