countably categorical structures

A countably infinite structure is called countably categorical (also called $\omega$ -categorical, or $\aleph_0$ -categorical) if all countable models of its first-order theory are isomorphic.

Ryll-Nardzewski, Engeler, and Svenonius proved that a countable structure is $\omega$ -categorical if and only if it has an oligomorphic automorphism group.