Cofinality of a linear order
= Cofinality of a linear order
{title2=$\operatorname{cf}(L)$}
The <cofinality of a linear order> is the least <cardinality> of a <cofinal subset>. It is preserved by order <isomorphisms>. The <order sum> of $\omega_1$ copies of the rational order has <cofinality> $\aleph_1$, whereas appending one final rational block changes its <cofinality> to $\aleph_0$ without changing its <cardinality> or the dense-linear-order axioms.