Definition:Free Occurrence

Definition

Let $\LL_1$ be the language of predicate logic.

Let $\mathbf A$ be a WFF of $\LL_1$.

An occurrence of a variable $x$ in $\mathbf A$ is said to be a free occurrence if and only if it is not bound.

Also known as

Some authors gloss over the difference between:

a free variable: a variable which exists in a WFF only as free occurrences

and:

a free occurrence of a variable which may otherwise exist as a bound variable.

Also see

• Definition:Occurrence (Formal Systems)
• Definition:Bound Occurrence, the complementary notion
• Definition:Alphabetic Substitution

Sources

• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 1$: Some mathematical language: Variables and quantifiers
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability: $\S 2.3$
• 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\mathrm{II}.5$ First-Order Logic Syntax: Definition $\mathrm{II}.5.5$