Elementary definition
Introduction 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
References * Mac Lane and Moerdijk, ''Sheaves in Geometry and Logic: A First Introduction to Topos Theory,'' page 4.