Definition:Algebraic (Model Theory)/Saturated Model

Definition

Let $\MM$ be an $\LL$-structure with universe $M$.

Let $A$ be a subset of $M$.

and let $\bar b$ be an ordered $n$-tuple of elements from $M$.

Let $\LL_A$ be the language formed by adding constant symbols to $\LL$ for each element of $A$.

Let $\MM$ be a saturated model.

Then $\bar b$ is algebraic over $A$ if and only if it has only finitely many images under $A$-automorphisms.

Also see

• Algebraic iff Finite Orbit

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