Definition:Definable/Set

Definition
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 $\MM$ there exists a formula $\map \phi x$ such that:
 * $a \in A \iff \MM \models \map \phi a$