Definition:Classes of WFFs/Plain WFF

A plain WFF of predicate calculus is a WFF with no parameters.

Thus $$WFF \left({\mathcal{P}, \varnothing}\right)$$ is the set of all plain WFFs formed from $$\mathcal{P}$$.

Note that a WFF with parameters from $\mathcal{K}$ is, by definition, a WFF whose parameters are all in $$\mathcal{K}$$.

That is, none of its parameters come from outside of $$\mathcal{K}$$.

Hence a plain WFF is a WFF with parameters from $\mathcal{K}$ for all $$\mathcal{K}$$.