Elementary theory
In mathematical logic, an elementary theory is a theory that involves axioms using only finitary first-order logic, without reference to set theory or using any axioms that have consistency strength equal to set theory.
Saying that a theory is elementary is a weaker condition than saying it is algebraic.
Examples
Examples of elementary theories include:- The theory of groups
- * The theory of finite groups
- * The theory of abelian groups
- The theory of fields
- * The theory of finite fields
- * The theory of real closed fields
- Axiomization of Euclidean geometry
Related
- Elementary definition
- Elementary theory of the reals