From sbelknap@UIC.EDU Fri Mar  3 18:26:47 2000
X-Digest-Num: 383
Message-ID: <44114.383.2192.959273826@eGroups.com>
Date: Fri, 3 Mar 2000 20:26:47 -0600
From: Steven Belknap <sbelknap@UIC.EDU>
Subject: pc has got it
X-Yahoo-Message-Num: 2192

>pc:
>1.  Call a set, s,  of clubs preclusive it being a member of any one of the
>clubs in s precludes being a member of any other club in s.
>2.  Call a set, m, of clubs maximally preclusive if it is preclusive and
>every proper superset of it is not preclusive (i.e., adding any other club to
>the set destroys its preclusivity - someone could belong to the new club as
>well as to some club in m set).
>Note, the empty set and all singletons are preclusive and some larrger sets
>may be.  But this is not yet necessarily sets of final clubs.  Each maximally
>preclusive set is final with repect to itself and some subset of the clubs,
>but not yet necessarily for the whole set of clubs.  However,
>3) the intersection of the set of all maximally preclusive sets (i.e., the
>set of clubs that are in every one of these max prec sets) is the set of
>final clubs for the whole set of clubs.  It is, of course, maximally
>preclusive and final over the whole set.
>So, the final clubs are those which are in all maximally preclusive sets of
>clubs.
>I think.
pc

Nicely done. I believe that you have defined final clubs. The 
"maximally preclusive" concept is the key. It might be easier to get 
your head around this for lojban translation purposes if expressed 
from the point of view of a single club. So a final club is any club 
which is in all maximally preclusive sets of clubs.

Steven

Steven Belknap, M.D.
Assistant Professor of Clinical Pharmacology and Medicine
University of Illinois College of Medicine at Peoria