Definition:Scope (Logic)/Quantifier

Definition
Let $\mathcal L_1$ be the formal language of predicate calculus.

Let $Q$ be an occurrence of a quantifier in $\mathbf A$.

Let $\mathbf B$ be a well-formed part of $\mathbf A$ such that $\mathbf B$ begins (omitting outer parentheses) with $Q x$.

That is, such that $\mathbf B = ( Q x: \mathbf C )$ for some WFF $\mathbf C$.

$\mathbf B$ is called the scope of the quantifier $Q$.

Also see
The scope of a given quantifier is unique, from Quantifier has Unique Scope.