\begin{definition}[Definition:Definable/Set]
Let $\MM$ be an $\LL$-structure with universe $M$.
Let $A$ be a subset of $M$.
Let $\LL_A$ be the language formed by adding constant symbols to $\LL$ for each element of $A$.
$A$ is a '''definable set''' in $\MM$ {{iff}} there exists a formula $\map \phi x$ such that:
:$a \in A \iff \MM \models \map \phi a$
\end{definition}