title: Elementary definition
text: # Elementary definition
  
  In mathematical logic, an elementary definition is a definition that can be made using only finitary first-order logic, and in particular without reference to set theory or using extensions such as plural quantification. Elementary definitions are of particular interest because they admit a complete proof apparatus while still being expressive enough to support most everyday mathematics (via the addition of elementarily-expressible axioms such as Zermelo–Fraenkel set theory (ZFC)).
  
  Saying that a definition is elementary is a weaker condition than saying it is algebraic.
  
  ## Related
  
  * Elementary sentence
  * Elementary theory
  