Axiom:Ordering Axioms/Class Formulation

Definition
Let $V$ be a basic universe.

Let $\RR \subseteq V \times V$ be a relation on $V$.

$\RR$ is an ordering in $V$ $\RR$ satisfies the axioms:

where $\Field \RR$ denotes the field of $\RR$.

These criteria are called the ordering axioms.

Also see

 * Axiom:Ordering Axioms/Formulation 1 for an alternative formulation of the ordering axioms on a set.
 * Definition:Ordering