Exercise 17, § 6

A cardinal $\aleph_\alpha$ is said to be regular (resp. singular) if the initial ordinal $\omega_\alpha$ is regular (resp. singular). For $\aleph_\alpha$ to be regular it is necessary and sufficient that for every family $(\mathfrak{a}_\iota)_{\iota \in I}$ of cardinals such that Card (I) $< \aleph_\alpha$ and $\mathfrak{a}_\iota < \aleph_\alpha$ for all $\iota \in I$, we have

$\aleph_\omega$ is the least singular cardinal.