title: Elementary theory
text: # 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
  
  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 sentence
  * Elementary definition
  * Elementary theory of the reals
  