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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.
![[icon]](#/media/File:Wiki_letter_w_cropped.svg){kind=small} | This section needs expansion. You can help by adding to it. (January 2021) |
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
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