Definition:Categorical (Model Theory)

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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.


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