Formula relativization to a class
= Formula relativization to a class
The relativization $\varphi^M$ of a formula $\varphi$ is obtained recursively by restricting every quantifier to $M$:
$$
(\exists x\,\psi)^M=\exists x\,(x\in M\land\psi^M),
\qquad
(\forall x\,\psi)^M=\forall x\,(x\in M\mathbin\Rightarrow\psi^M).
$$
For parameters in $M$, the ambient statement $\varphi^M$ holds exactly when the structure $(M,\in)$ satisfies $\varphi$.