countably categorical structures

A countably infinite structure is called countably categorical (also called $\omega$-categorical, or ${\mathrm{\aleph }}_{\mathrm{0}}$-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
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	${\mathrm{\aleph }}_0$-categorical
Synonym	$\omega$-categorical
Related topic	oligomorphicPermutationGroup
Related topic	OligomorphicPermutationGroup