Definition:Singular Cardinal

Definition

Let $\kappa$ be an infinite cardinal.

Then $\kappa$ is a singular cardinal if and only if $\map {\mathrm {cf} } \kappa < \kappa$.

That is, the cofinality of $\kappa$ is less than itself.

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Also see

• Regular Cardinal

Sources

• 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 10.65 \ (2)$