|WikiProject Mathematics||(Rated Start-class, Mid-importance)|
[...]the non-existence of an antichain A of size n+1 in S is a necessary and sufficient condition for S to be the union of n total orders. That doesn't sound quite right. Surely, if S has no antichain of size n+1, then it doesn't have one of size n+2 either, and by this equivalence it would then be the union of n and n+1 total orders at the same time; in fact we could continue this reasoning to conclude that S is the union of n, n+1, n+2, ... total orders. Presumably the equivalence holds only for the minimal such n? --Eriatarka 13:29, 15 January 2006 (UTC)
Some combinatorics articles, some mathematical logic articles, and some algebra articles probably ought to link to this page. Michael Hardy 00:16, 25 Oct 2003 (UTC)
Agreed. Don't think Dilworth's theorem is here? Or Sperner's lemma?
Charles Matthews 09:50, 25 Oct 2003 (UTC)
I think the definition of join and meet are both broken, and should be defined as follows: