Definition:Classes of WFFs/Plain WFF
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However immediate, this goes on a proof page
Definition
A plain WFF of predicate logic is a WFF with no parameters.
Thus $WFF \left({\mathcal P, \mathcal F, \varnothing}\right)$ is the set of all plain WFFs with relation symbols from $\mathcal P$ and function symbols from $\mathcal F$.
However immediate, this goes on a proof page
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It is immediate that a plain WFF is a WFF with parameters from $\mathcal K$ for all choices of $\mathcal K$.
Sources
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability: $\S 2.3$