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Home > Strongly inaccessible cardinal

In other words

1. the cofinality cf(κ) = κ, and
2. 2^λ < 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

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Topics: Strongly Inaccessible Cardinal Kappa Zfc Assumption Cardinals...

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Strongly inaccessible cardinalIn 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 tha Strongly connected componentA directed graph is called strongly connected if for every pair of vertices u and v there is a path from u to v and a path from v to u. The strongly connected components SCC of a directed graph are its maximal strongly connected subgraphs. Strongly-typed programming languageIn computing, strongly-typed when applied to a programming language, is used to describe how the language handles datatypes. Strongly-typed" may have one of several incompatible meanings, depending on context. A programming language that is not strongly-t