Definition:Axiomatization/Axiom

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. Let $\mathcal A$ be an axiomatization of $\mathcal F$.

Then a formula $\phi \in \mathcal A$ is called an axiom.