# Definition:Model (Logic)/Set of Logical Formulas

## Definition

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

Let $\mathcal M$ be a structure of $\mathscr M$.

Let $\mathcal F$ be a set of logical formulas of $\mathcal L$.

Then $\mathcal M$ is a model of $\mathcal F$ iff:

$\mathcal M \models_{\mathscr M} \phi$ for every $\phi \in \mathcal F$

that is, if it is a model of every logical formula $\phi \in \mathcal F$.