From cburke@MITRE.ORG Fri Mar 3 13:20:42 2000 X-Digest-Num: 383 Message-ID: <44114.383.2175.959273826@eGroups.com> Date: Fri, 03 Mar 2000 16:20:42 -0500 From: Carl Burke Subject: Re: final clubs Jorge Llambias wrote: ... > Definition: Every club is a final club. > > To disprove it all you have to do is find a configuration > where some clubs are not final and yet final clubs are > well defined. I don't think there is one. Suppose we have the following situation: Club A imposes no conditions on its members Club B requires members to swear a loyalty oath, and to swear no other oaths Club C requires members to swear a loyalty oath, and to swear no other oaths The set of final clubs is well-defined, and is composed of clubs B and C (the set of clubs which require loyalty oaths); membership in club A neither precludes nor is precluded by membership in clubs B or C. This doesn't help us find a non-recursive definition of 'final club', but it does illustrate that not all clubs are necessarily final. -- Carl Burke cburke@mitre.org