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)

Disambig or not
I have revisited this suite of pages.

I actually don't recommend Definition:Complete Ordered Set to be a disambig, for the reasons:
 * a) we already have Definition:Complete, which should suffice (and has now been expanded as appropriate in our house style to make it more useful)
 * b) as a complete ordered set is a well-defined concept in its own right, it merits its own page, and it is not clear how the disambig would work here
 * c) we can include the different types of "completely ordered" in the "also see" section, as I have done.

I think what I've put together should work as a general strategy. --prime mover (talk) 03:18, 14 February 2018 (EST)

Merge or not
I say no to the merge, as an ordered set is not (necessarily) a lattice. So while a "complete lattice" is an instance of a "complete ordered set", if anything the connection should be at the "Lattice" end: a "Complete Lattice" is a "lattice" which is also a "complete ordered set". --prime mover (talk) 03:22, 14 February 2018 (EST)