Categorical theory
= Categorical theory
{title2=$\kappa$-categorical}
{wiki}
A <first-order theory> is $\kappa$-categorical when it has a <model of a first-order theory> of <cardinality> $\kappa$ and any two such <models of a first-order theory> are <isomorphic>. Existence is required, so a missing model size does not make categoricity vacuously true.