Axiom:Ordering Axioms

Definition
Let $S$ be a set.

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

Formulation 1
$\RR$ satisfies the ordering axioms $\RR$ satisfies the axioms:

Formulation 2
$\RR$ satisfies the ordering axioms $\RR$ satisfies the axioms:

Class Theory
Let $V$ be a basic universe.

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

$\RR$ satisfies the ordering axioms $\RR$ satisfies the axioms:

Also see

 * Equivalence of Definitions of Ordering