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Strongly inaccessible cardinal
In mathematics, a strongly inaccessible cardinal is an uncountable cardinal number κ that is regular and a strong limit cardinal.
In other words
- the cofinality cf(κ) = κ, and
- 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 if and only if it is weakly inaccessible.
The assumption of the existence of a strongly inaccessible cardinal is sometimes applied in the form of the assumption that one can work inside a Grothendieck universe, the two ideas being intimately connected
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details