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.

Sources

• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 1$: Some mathematical language: Axiom systems