Definition:Finitely Satisfiable

Definition
Let $\mathcal L$ be a logical language.

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

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

Then $\mathcal F$ is finitely satisfiable for $\mathscr M$ :


 * For each finite subset $\mathcal F' \subseteq \mathcal F$, there is some $\mathscr M$-model $\mathcal M$ of $\mathcal F'$

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


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

Also see

 * Definition:Satisfiable Set of Formulas


 * Compactness Theorem