First-order language

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

A set of constants, such as A, B, C, ...
A set of n-ary relations such as >(x, y).
A set of n-ary functions such as +(x, y).
An infinite set of variables such as x, y, z,...
The connectives $\text{[math]}$ , $\text{[math]}$ .
quantifiers: $\text{[math]}$ , $\text{[math]}$ .
parenthesis: $\text{[math]}$ , $\text{[math]}$ .
The equality symbol $\text{[math]}$ .

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

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