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From: gil@daffy.gatech.edu (Gil Neiger)
Newsgroups: comp.theory
Subject: Name for a Relation?
Message-ID: <824@mephisto.edu>
Date: 8 Feb 91 21:12:18 GMT
Sender: news@gatech.edu
Reply-To: gil@cc.gatech.edu (Gil Neiger)
Organization: College of Computing, Georgia Institute of Technology
Lines: 22

I am dealing with a kind of relation and I'm wondering if there's
a name for it.  It's a binary relation that is irreflexive, transitive
and antisymmetric (in other words, it's a partial order that's
irreflexive).  Added to this I have the following condition:  the
"not related" relation is an equivalence class.

More formally, suppose that my relation is denoted by "<".  Define
"not related," using the symbol "|" as follows:

	(p | q) if and only if (not(p < q) and not(q < p))

My relation < has the property that

	if p|q and q|r, then p|r.

Thus, the "not related" relation (|) is transitive; since < is
irreflexive, | is reflexive; by definition it is symmetric.

Given all this, is there a name for the relation "<"?

				- GIl Neiger
				gil@cc.gatech.edu