Definition:Strict Partial Ordering

Definition
Let $\struct {S, \prec}$ be a relational structure.

Let $\prec$ be a strict ordering.

Then $\prec$ is a strict partial ordering on $S$ $\prec$ is not connected.

That is, $\struct {S, \prec}$ has at least one pair which is non-comparable:
 * $\exists x, y \in S: x \nprec y \land y \nprec x$

Also known as
Some sources call this an antireflexive partial ordering.