Definition:Falsifiable/Set of Formulas

Definition
Let $\mathcal L$ be a logical language.

Let $\mathscr M$ be a formal semantics for $\mathcal L$.

A collection $\mathcal F$ of logical formulas of $\mathcal L$ is falsifiable for $\mathscr M$ iff:


 * Some $\mathscr M$-structure $\mathcal M$ is not a model of $\mathcal F$

That is, there exists some structure $\mathcal M$ of $\mathscr M$ such that:


 * $\mathcal M \not\models_{\mathscr M} \mathcal F$