From pycyn@aol.com Fri Mar 3 17:19:13 2000
X-Digest-Num: 383
Message-ID: <44114.383.2189.959273826@eGroups.com>
Date: Fri, 3 Mar 2000 20:19:13 EST
From: pycyn@aol.com
Subject: Final clubs.
This is the sort of thing that usually works for these types of critters.
sorry it is not in Lojban, it is hard enough in English.
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