Definition:Universal Closure of Well-Formed Formula
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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 $\text{II}.5.6$