Definition:Finitely Satisfiable

Definition

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 $\mathscr M$ if and only if:

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:

$\MM \models_{\mathscr M} \FF'$

Also see

• Definition:Satisfiable Set of Formulas

• Compactness Theorem