# oligomorphic permutation group

A permutation group acting on a countably infinite set is called oligomorphic, if it has finitely many orbits of $n$-tuples, for all $n\geq 1$.

Ryll-Nardzewski, Engeler, and Svenonius proved that a countably infinite first-order structure has an oligomorphic automorphism group if and only if the structure is $\omega$-categorical.

Title oligomorphic permutation group OligomorphicPermutationGroup 2013-03-22 15:15:36 2013-03-22 15:15:36 amador (8479) amador (8479) 6 amador (8479) Definition msc 03C35 CountablyCategoricalStructures oligomorphic automorphism group