Recursively Categorical Linear Orderings

A recursive structure <!-- MATH $\mathcal{A}$ --> is recursively categorical if every recursive structure <!-- MATH $\mathcal{A}'$ --> isomorphic to <!-- MATH $\mathcal{A}$ --> is recursively isomorphic to <!-- MATH $\mathcal{A}$ --> . We classify the recursively categorical linear orderings as precisely those recursive linear orderings which have only finitely many elements with an immediate successor.