I'm trying to find an effective and making sense way (for programming purposes, but also from math interest) to order partial orders, means, given a set and many partial orders (trees) over it. How can those partial orders be "naturally" ordered?
Specifically, I'm interested in ordering partial orders which each one of them has a Hasse diagram of a tree. Moreover, in my case of interest, for every $a\leq b$ there exists c such that a=b-c can be defined (in some too specific way my trees are built) and $c\leq b$ (almost like "Monus").