\begin{definition}[Definition:Algebraic (Model Theory)]
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 $A$.
$\bar b$ is '''algebraic''' over $A$ {{iff}} there is an $\LL_A$-formula $\map \phi {\bar x}$ with $n$ free variables such that:
:$\MM \models \map \phi {\bar b}$
and:
:the set $\set {\bar m \in M^n : \MM \models \map \phi {\bar m} }$ has only finitely many elements.
{{Disambiguate|Definition:Logical Formula}}
\end{definition}