First-Order Language

A First-order language in Zermelo-Fraenkel set theory consists of the following symbols:

1. A set of constants, such as A, B, C, ...
2. A set of n-ary relations such as >(x, y).
3. A set of n-ary functions such as +(x, y).
4. An infinite set of variables such as x, y, z,...
5. The connectives , .
6. quantifiers: , .
7. parenthesis: , .
8. The equality symbol .

First-order languages are used to describe mathematics in mathematical notation with mathematical formulae.