Definition:Axiom/Formal Systems/Axiom Schema

Definition
Let $\mathcal F$ be a formal system.

An axiom schema is a formula in $\mathcal F$ containing one or more variables which are outside $\mathcal F$ itself.

This formula can then be used to represent an infinite number of individual axioms in one statement.

If $\mathcal F$ does not require an axiom schema in order to be represented, then it is called finitely axiomatizable.

Linguistic Note
The plural of axiom schema is correctly axiom schemata, but it is commonplace to see the word schemas used for schemata.

Examples
It was proved by Richard Montague in 1957 that ZFC and Peano arithmetic require an axiom schema.