From: Paul Levy <pbl@cs.bham.ac.uk>
To: categories list <categories@mta.ca>
Subject: ordinal dependent choice
Date: Tue, 28 Jun 2011 14:12:22 +0100 [thread overview]
Message-ID: <E1QbemH-0007q1-45@mlist.mta.ca> (raw)
Dear all,
Let alpha be an ordinal. Let $alpha be the totally ordered set of
ordinals below alpha.
"Alpha-dependent choice" is the following statement:
for any functor A : $alpha ^ op ---> Set,
if A_i is nonempty for all i < alpha,
and A_i,j : A_j ---> A_i is surjective for all i <= j < alpha,
then the limit of A is nonempty.
If alpha has a cofinal omega-sequence (i.e. an omega-sequence of
ordinals < alpha whose supremum is alpha), then alpha-dependent choice
follows from dependent choice.
I would think that, if alpha doesn't have a cofinal omega-sequence,
then alpha-dependent choice is false. Is there a known
counterexample? E.g. in the case alpha = omega_1 (the least
uncountable ordinal).
Thanks,
Paul
--
Paul Blain Levy
School of Computer Science, University of Birmingham
+44 (0)121 414 4792
http://www.cs.bham.ac.uk/~pbl
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2011-06-28 13:12 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-06-28 13:12 Paul Levy [this message]
2011-06-29 8:32 ` N.Bowler
2011-06-29 9:12 ` Prof. Peter Johnstone
2011-06-30 16:07 ` Paul Levy
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