Definition:Stability (Model Theory)/Kappa-Stable Structure

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Definition

Let $\kappa$ be an infinite cardinal.

Let $\mathcal M$ be an $\mathcal L$-structure.

Let $\operatorname {Th} \left({\mathcal M}\right)$ be the $\mathcal L$-theory of $\mathcal M$.


$\mathcal M$ is $\kappa$-stable if $\operatorname{Th} \left({\mathcal M}\right)$ is $\kappa$-stable.