\begin{definition}[Definition:Definable/Element]
Let $\MM$ be an $\LL$-structure with universe $M$.
Let $A$ be a subset of $M$.
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 '''definable''' over $A$ if there is an $\LL_A$-formula $\map \phi {\bar x}$ with $n$ free variables such that the set $\set {\bar m \in M^n :\MM \models \map \phi {\bar m} }$ contains $\bar b$ but nothing else.
\end{definition}