# 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.

Title countably categorical structures CountablyCategoricalStructures 2013-03-22 15:15:38 2013-03-22 15:15:38 amador (8479) amador (8479) 5 amador (8479) Derivation msc 03C35 $\aleph_{0}$-categorical $\omega$-categorical oligomorphicPermutationGroup OligomorphicPermutationGroup