First-order axiomatizable class

A class of structures is first-order axiomatizable when it is exactly the class of models of some first-order theory. If extra constants are allowed, the corresponding class of reducts consists of structures that admit interpretations of those constants satisfying the theory.

The torsion-free groups are axiomatized by the group axioms together with, for every integer $n\ge 2$,

In the language with $\le$, total orders are axiomatized by reflexivity, antisymmetry, transitivity, and totality