Definition:Scope (Logic)/Quantifier
Jump to navigation
Jump to search
Definition
Let $\mathbf A$ be a WFF of the language of predicate logic.
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 $\mathbf B = \paren {Q x: \mathbf C}$ for some WFF $\mathbf C$.
$\mathbf B$ is called the scope of the quantifier $Q$.
Also see
Sources
- 1972: Patrick Suppes: Axiomatic Set Theory (2nd ed.) ... (previous) ... (next): $\S 1.2$ Logic and Notation
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability: $\S 2.3$: Theorem $2.3.1$