strict partial order

A strict partial order is a homogeneous relation that is irreflexive, antisymmetric, and transitive.

Formally,
a binary relation $<$ over a set $S$ is a strict partial order if for all $a,b,c$ in $S$,

• $a\nless a$ (irreflexive)
• if $a<b$ and $b<c$ then $a<c$ (transitive)
• if $a<b$ then $b\nless a$ (antisymmetric)