Definition:Axiom/Formal Systems/Axiom Schema

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

An axiom schema (plural: axiom schemata) 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 a countably 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.

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