Definition talk:Complete Lattice/Definition 2

Merge?
I vote we turn this into a disambiguation page, probably synonymous with Definition:Complete Ordering. There are:


 * Dedekind completeness
 * Bounded completeness (Dedekind both directions)
 * dcpo (often called just cpo)
 * Complete lattice
 * Wikipedia also mentions omega-complete partial order, but I haven't encountered that elsewhere yet, personally, which of course doesn't mean it's not real.

So ... might be good to organize these things. --Dfeuer (talk) 00:53, 10 January 2013 (UTC)


 * Sounds good to me.
 * By the way, bounded completeness is not the same as Dedekind completeness in both directions; Dedekind completeness is a self-dual property. --abcxyz (talk) 01:28, 10 January 2013 (UTC)


 * Headdesk. Sorry 'bout that... I got very little sleep and have a headache. --Dfeuer (talk) 01:52, 10 January 2013 (UTC)


 * First of all, the disambig you propose should probably reside at "Complete Ordered Set". $\omega$-completeness is that every chain has an upper bound (or lower, whichever matches the categorical notion). Awodey speaks of it but I haven't covered that yet. --Lord_Farin (talk) 08:48, 10 January 2013 (UTC)
 * Oh, and I forgot to say I'm supporting the idea. --Lord_Farin (talk) 08:49, 10 January 2013 (UTC)