Definition:Categorical (Model Theory)

Definition
Let $T$ be an $\mathcal{L}$-theory.

Let $\kappa$ be a cardinal.

$T$ is $\kappa$-categorical if whenever $\mathcal{M}$ and $\mathcal{N}$ are models of $T$ of cardinality $\kappa$, then $\mathcal{M}$ and $\mathcal{N}$ are isomorphic.