From: categories <cat-dist@mta.ca>
To: categories <categories@mta.ca>
Subject: Re: Challenge from Harvey Friedman
Date: Sat, 24 Jan 1998 13:34:43 -0400 (AST) [thread overview]
Message-ID: <Pine.OSF.3.90.980124133433.27531F-100000@mailserv.mta.ca> (raw)
Date: Sat, 24 Jan 1998 15:59:46 +0000 (GMT)
From: Dr. P.T. Johnstone <P.T.Johnstone@dpmms.cam.ac.uk>
> But the axioms of elementary topoi are already incomparably more
> complicated than the axioms for set theory presented here.
What on earth does Friedman mean by complicated? As Peter Freyd
pointed out a long time ago, the axioms for an elementary topos are
essentially algebraic -- that is, they live at a very low level
of logical complexity. The very first axiom in anyone's (including
Friedman's) axiomatization of set theory is the axiom of
extensionality, which is not expressible even in coherent logic
(at least, not unless you take not-membership as a primitive
predicate, on the same level as membership).
Unless Friedman can put forward an objective measure of complexity
(as opposed to "unfamiliarity to H. Friedman") which justifies the
above quote, then his challenge is not worth considering.
Peter Johnstone
next reply other threads:[~1998-01-24 17:34 UTC|newest]
Thread overview: 11+ messages / expand[flat|nested] mbox.gz Atom feed top
1998-01-24 17:34 categories [this message]
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