From pycyn@aol.com Fri Mar 3 18:23:51 2000 X-Digest-Num: 383 Message-ID: <44114.383.2191.959273826@eGroups.com> Date: Fri, 3 Mar 2000 21:23:51 EST From: pycyn@aol.com Subject: Final Clubs oops OK so it doesn't quite work yet. The club structure Jorge and all have been fussing with shows this, since {A} is a maximally proclusive set, as {B,C}, so the set of final clubs is the null, when it ought to have been {B, C} or {A} or something. Or maybe not. But there is soemthing else clearly wrong about that definition of mine (based on similar problems but apparently not perfectly similar ones): the intersection will obviously not in general be maximally proclusive, since it is in several presumably larger set which are maximal, so adding any of the dropped items will not make it lose it proclusivity. We could avoid the first problem by requiring that there actually be precluded pairs, I suppose. And the last is not really a problem, only a peculiarity: that there could in general be more final clubs than there are, but that there would not then be a unique definition of which clubs are final. Given that there is such a definition (the basis of the problem), these two factors seem required. Now, is there a solution that doesn't require this metaproblematic adhocery? pc