From pycyn@aol.com Mon Mar 06 06:52:32 2000 Received: (qmail 18649 invoked from network); 6 Mar 2000 14:52:48 -0000 Received: from unknown (10.1.10.27) by m1.onelist.org with QMQP; 6 Mar 2000 14:52:48 -0000 Received: from unknown (HELO imo13.mx.aol.com) (152.163.225.3) by mta2.onelist.org with SMTP; 6 Mar 2000 14:52:48 -0000 Received: from Pycyn@aol.com by imo13.mx.aol.com (mail_out_v25.3.) id h.a0.1f11ea7 (8329) for ; Mon, 6 Mar 2000 09:52:45 -0500 (EST) Message-ID: Date: Mon, 6 Mar 2000 09:52:45 EST Subject: Re:[Lojban](unknown) Addendum To: lojban@onelist.com MIME-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Mailer: AOL 4.0 for Windows sub 30 X-eGroups-From: Pycyn@aol.com From: pycyn@aol.com To the result add that there are at least two mutually excluding clubs. If there are not, there is not a unique solution even with the global requirement of preclusion. Then any club by itself could be final. I made the changes to get rid of xorxes' result that the final club had to be the set of all clubs to reachable by the definition -- this seemed wrong: (A, B) mutually preclusive, C precluded by neither and, indeed, with two members, one in A, the other in B. But {C} is a maximally preclusive set in the original sense and so would mean the definition gave no solution here. I suppose this amounts to taking the definition as having existential import, which, as you know, I seldom have much trouble doing. The union of maximally preclusive sets, by the bye, is not maximally preclusive, since it is a superset to each of the maximally preclusive sets. pc