Definition:Model (Logic)/Set of Logical Formulas

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

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

Let $\FF$ be a set of logical formulas of $\LL$.

Then $\MM$ is a model of $\FF$ if and only if:

$\MM \models_{\mathscr M} \phi$ for every $\phi \in \FF$

that is, if and only if it is a model of every logical formula $\phi \in \FF$.

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