From pycyn@aol.com Mon Mar 06 06:36:56 2000 Received: (qmail 20591 invoked from network); 6 Mar 2000 14:37:12 -0000 Received: from unknown (10.1.10.26) by m3.onelist.org with QMQP; 6 Mar 2000 14:37:12 -0000 Received: from unknown (HELO imo24.mx.aol.com) (152.163.225.68) by mta1.onelist.com with SMTP; 6 Mar 2000 14:37:12 -0000 Received: from Pycyn@aol.com by imo24.mx.aol.com (mail_out_v25.3.) id h.2.1678c51 (1813) for ; Mon, 6 Mar 2000 09:37:08 -0500 (EST) Message-ID: <2.1678c51.25f51c94@aol.com> Date: Mon, 6 Mar 2000 09:37:08 EST Subject: Re: [lojban] (unknown) 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 Well, it does seem that we need the requirement that (interesting) maximally preclusive sets contain more than one member, else a set that is not at all preclusive is (sole) member of a maximally preclusive set, its singleton (there is no other member so the condition is vacuously satisfied). So, add to the definition of maximally preclusive that there is more than one member. THEN we get the interesting result that, if the given definition alone manages to pick out a unique final set, every club that precludes another club precludes all other clubs that preclude clubs (if x precludes y and z precludes w, then x precludes z and w as well -- assuming x, z, and w are distinct). If the definition fails then a set of clubs is selected as final by some means not mentioned in the "definition" -- any maximally prelusive set will do. Or, for that matter, the singleton of any non-preclusive club (vacuously again). pc