Definition:Classes of WFFs/Plain Sentence

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Let $\mathcal L_1$ be the language of predicate logic.

A WFF is said to be a plain sentence iff it is both plain and a sentence.

That is, if it contains free variables nor parameters.

Thus, plain sentences are those WFFs which are in $SENT \left({\mathcal P, \mathcal F, \varnothing}\right)$.