Re: final clubs

[Carl Burke <cburke@MITRE.ORG>]

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