oligomorphic permutation group

A permutation groupMathworldPlanetmath acting on a countably infiniteMathworldPlanetmath set is called oligomorphic, if it has finitely many orbits of n-tuples, for all n1.

Ryll-Nardzewski, Engeler, and Svenonius proved that a countably infinite first-order structureMathworldPlanetmath has an oligomorphic automorphism group if and only if the structure is ω-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