28 Jul
2009
28 Jul
'09
2:06 p.m.
On Mon, 27 Jul 2009 05:05:59 PM EDT, Andrej Bauer <andrej.bauer@andrej.com> asked:
So what does a chain-complete poset which isn't complete look like?
Take the product of any nonempty discrete poset X with the ordinal 2. Give Xx2 the "product order" ((x, a) </= (y, b) iff x=y and a </= b). The only non-singleton nonempty chains are the subsets {x} x 2 . Clearly each of these is complete, Xx2 is chain-complete, and yet Xx2 is not at all complete -- not even a semilattice either way. HTH. Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]