In mathematical logic, an elementary definition is a definition that can be made using only finitary firstorder 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 elementarilyexpressible axioms such as ZFC).
Saying that a definition is elementary is a weaker condition than saying it is algebraic.
