countably categorical structures

A countably infinite structure is called countably categorical (also called $\omega$-categorical, or ${\mathrm{\aleph }}_{\mathrm{0}}$-categorical)if all countable models of its first-order theory are isomorphic.

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