Definition:Regular Cardinal

Definition

Let $\kappa$ be an infinite cardinal.

Then $\kappa$ is a regular cardinal if and only if:

$\map {\mathrm {cf} } \kappa = \kappa$

That is, if and only if the cofinality of $\kappa$ is equal to itself.

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Also see

• Definition:Singular Cardinal
• Definition:Weakly Inaccessible Cardinal
• Definition:Strongly Inaccessible Cardinal

Sources

• 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 10.65 \ (1)$