Definition ($L$-formula with parameters from $A$). Given a language $L$, an $L$-structure $M$ and a subset $A\subseteq M$, we call an $L_A$-formula an $L$-formula with parameters from $A$.

Write these as $\phi (\overline{x},\overline{a})$ for $\phi (\overline{x},\overline{y})$ an $L$-formula, and $\overline{a}\in A$ (identify with ${\underline{a}}^M$).