countably categorical structures

A countably infiniteMathworldPlanetmath structureMathworldPlanetmath is called countably categorical (also called ω-categorical, or 0-categorical) if all countableMathworldPlanetmath models of its first-order theory are isomorphicPlanetmathPlanetmath.

Ryll-Nardzewski, Engeler, and Svenonius proved that a countable structure is ω-categorical if and only if it has an oligomorphic automorphism group.

Title countably categorical structures
Canonical name CountablyCategoricalStructures
Date of creation 2013-03-22 15:15:38
Last modified on 2013-03-22 15:15:38
Owner amador (8479)
Last modified by amador (8479)
Numerical id 5
Author amador (8479)
Entry type Derivation
Classification msc 03C35
Synonym 0-categorical
Synonym ω-categorical
Related topic oligomorphicPermutationGroup
Related topic OligomorphicPermutationGroup