Definition:Scope of Occurrence

This page is about the scope of an occurrence. For other uses, see Definition:Scope.

Definition

Let $\mathcal F$ be a formal language with alphabet $\mathcal A$.

Let $\mathbf A$ be a well-formed formula of $\mathcal F$.

Let $a$ be a fixed occurrence of some element of $\mathcal A$ in $\mathbf A$.

Then the scope of $a$ is the smallest well-formed part of $\mathbf A$ that contains $a$.

Also see

• Definition:Scope (Logic), highlighting two of the most common usages of scopes

Sources

• 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\mathrm{II}.4$ Polish Notation: Definition $\mathrm{II}.4.6$