\begin{definition}[Definition:Finitely Satisfiable]
Let $\LL$ be a logical language.
Let $\mathscr M$ be a formal semantics for $\LL$.
Let $\FF$ be a collection of logical formulas of $\LL$.
Then $\FF$ is '''finitely satisfiable for $\mathscr M$''' {{iff}}:
:For each finite subset $\FF' \subseteq \FF$, there is some $\mathscr M$-model $\MM$ of $\FF'$
That is, for each such $\FF'$, there exists some structure $\MM$ of $\mathscr M$ such that:
:$\MM \models_{\mathscr M} \FF'$
\end{definition}