Definition:Finitely Axiomatizable

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

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

Let $\mathcal F$ be an $\mathcal L$-theory.

Then $\mathcal F$ is called finitely axiomatizable iff there exists a finite axiomatization $\mathcal A$ of $\mathcal F$.