Definition:Axiomatization

Definition
Let $\LL$ be a logical language.

Let $\mathscr M$ be a formal semantics for $\LL$.

Let $\FF$ be an $\LL$-theory.

An axiomatization of $\FF$ is a subset $\AA \subseteq \FF$ such that:


 * $\FF = \set {\phi \in \LL: \AA \models_{\mathscr M} \phi}$

That is, all of $\FF$ is a semantic consequence of $\AA$.