Editing Axiom schema (section)

==Finite axiomatization==
Given that the number of possible subformulas or terms that can be inserted in place of a schematic variable is infinite, an axiom schema stands for an infinite [[class (set theory)|class]] or set of axioms. This set can often be [[recursive definition|defined recursively]]. A theory that can be axiomatized without schemata is said to be '''finitely axiomatizable'''.

===Finitely axiomatized theories===
All theorems of [[ZFC]] are also theorems of [[von Neumann–Bernays–Gödel set theory]], but the latter can be finitely axiomatized. The set theory [[New Foundations]] can be finitely axiomatized through the notion of [[stratification (mathematics)|stratification]].