Aleph-one-like linear order
= Aleph-one-like linear order
{title2=$|L|=\aleph_1,\quad|L_{<x}|\le\aleph_0$}
An <aleph-one-like linear order> has size $\aleph_1$ and every point has only countably many predecessors. Consequently every proper initial segment is countable, since it is bounded by any point outside it. This differs from requiring every nonempty interval to be uncountable.