Strict partial order

Set

context $X$
definiendum $ <\ \in\ \text{StrictPartOrd}(X) $
context $ <\ \in\ \mathrm{Rel}(X) $
$ x,y,z\in X $
postulate $ x \nless x $
postulate $ x<y\land y<z \implies x<z $

Here we use infix notation: $x<y\ \equiv\ <(x,y)$.

Discussion

A strict partial order is automatically anti-symmetric.

Reference

Wikipedia: Order theory, Poset

Parents

Subset of

Reflexive relation, Transitive relation, Anti-symmetric relation