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 which have consistency strength equal to set theory.

Saying that a theory is elementary is a weaker condition than saying it is algebraic.

Examples[edit]

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

Related[edit]

• Elementary sentence
• Elementary definition
• Elementary theory of the reals

References[edit]

• Mac Lane and Moerdijk, Sheaves in Geometry and Logic: A First Introduction to Topos Theory, page 4.

This mathematical logic-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e