10 Mar
2006
10 Mar
'06
9:47 p.m.
Franklin wrote: << OK. I'm still refining this problem. The problem now is to describe a maximal uncountable antichain of subsets of Z, where no component set is either finite or counter-finite (i.e., Z-S must not be finite). And yes, I chose the word describe deliberately; the existence of such a set is easy to establish
Hey, you could've said "nice example" when I solved your last question (:-)>. Anyhow, I've found as cute a little antichain as you could ask for that consists solely of subsets of Z that are each infinite and co-infinite. (I'm not sure how hard this is, but it seemed hard to me.) Without Zorn's Lemma, however, I don't yet see how to extend it to a maximal antichain. --Dan