Definition:Universal Closure of Well-Formed Formula

Definition

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

Let $\mathbf A$ be a well-formed formula of $\LL_1$.

A universal closure of $\mathbf A$ is a sentence $\mathbf B$ of $\LL_1$ of the form:

$\forall x_1: \cdots \forall x_n: \mathbf A$

By definition of sentence, this means that at least the variables occurring freely in $\mathbf A$ should be quantified over.

Sources

• 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\text{II}.5$ First-Order Logic Syntax: Definition $\text{II}.5.6$