$\kappa$-categorical

Let $L$ be a first order language and let $S$ be a set of $L$-sentences. If $\kappa$ is a cardinal, then $S$ is said to be if $S$ has a model of cardinality $\kappa$ and any two such models are isomorphic.

In other words, $S$ is categorical iff it has a unique model of cardinality $\kappa$, to within isomorphism.

Title	$\kappa$-categorical
Canonical name	kappacategorical
Date of creation	2013-03-22 13:00:33
Last modified on	2013-03-22 13:00:33
Owner	Evandar (27)
Last modified by	Evandar (27)
Numerical id	4
Author	Evandar (27)
Entry type	Definition
Classification	msc 03C35
Related topic	VaughtsTest
Related topic	ExampleOfUniversalStructure