Definition:Axiomatic System

An axiomatic system is a system of logic or mathematics which possesses an explicitly stated set of axioms from which theorems can be derived.

There are several axiomatic systems of logic, most of which produce the same logical structure.

The most well-known axiomatic system of mathematics is that based on the Zermelo-Fraenkel axioms. There are in fact two separate systems ZF and ZFC, the latter being "ZF with the Axiom of Choice included."