Definition:Satisfiable/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 satisfiable for $\mathscr M$ iff:


 * There is some $\mathscr M$-model $\mathcal M$ of $\mathcal F$

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


 * $\mathcal M \models_{\mathscr M} \mathcal F$