Definition:Falsifiable/Set of Formulas

Definition

Let $\LL$ be a logical language.

Let $\mathscr M$ be a formal semantics for $\LL$.

A collection $\FF$ of logical formulas of $\LL$ is falsifiable for $\mathscr M$ if and only if:

Some $\mathscr M$-structure $\MM$ is not a model of $\FF$

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

$\MM \not\models_{\mathscr M} \FF$

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