Definition:Classes of WFFs

Definition
Let $\mathcal L_1$ denote the formal language of predicate calculus. The set of all WFFs of $\mathcal L_1$ formed with relation symbols from $\mathcal P$ and function symbols from $\mathcal F$ can be denoted $WFF \left({\mathcal P, \mathcal F}\right)$.

If so desired, the parameters can also be emphasized by writing $WFF \left({\mathcal P, \mathcal F, \mathcal K}\right)$ instead.

To specify $\mathcal P$, one speaks of WFFs with relation symbols from $\mathcal P$.

To specify $\mathcal F$, one speaks of WFFs with function symbols from $\mathcal F$.

To specify $\mathcal K$, one speaks of WFFs with parameters from $\mathcal K$.

Of course, combinations of these are possible.

Several classes of WFFs are often considered and have special names.