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 $n\ge 1$.

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
Canonical name	OligomorphicPermutationGroup
Date of creation	2013-03-22 15:15:36
Last modified on	2013-03-22 15:15:36
Owner	amador (8479)
Last modified by	amador (8479)
Numerical id	6
Author	amador (8479)
Entry type	Definition
Classification	msc 03C35
Related topic	CountablyCategoricalStructures
Defines	oligomorphic automorphism group