\begin{definition}[Definition:Axiomatization]
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 $\AA$.
\end{definition}