# $\kappa$-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 kappacategorical 2013-03-22 13:00:33 2013-03-22 13:00:33 Evandar (27) Evandar (27) 4 Evandar (27) Definition msc 03C35 VaughtsTest ExampleOfUniversalStructure