Inconsistencies in Cartesian Closed Categories

• To: types@THEORY.LCS.MIT.EDU
• Subject: Inconsistencies in Cartesian Closed Categories
• From: Albert R. Meyer <meyer@THEORY.LCS.MIT.EDU>
• Date: Tue, 2 Aug 88 22:52:23 edt

Date: Mon, 1 Aug 88 15:57:30 BST
From: Paul Taylor <mcvax!doc.ic.ac.uk!pt@uunet.UU.NET>

There are numerous "folklore" results about inconsistencies between
cccs with fixpoints and various logical operations (negation, coproduct,
conjunction, natural numbers).  None of these (apart, perhaps, from
the result in my joint paper with Andrew Pitts about type-of-types
and equality) is particularly remarkable, but they ought, nevertheless,
to be available in the literature.  They were discussed briefly in my
thesis, and also in a technical report by Huwig & Poigne, and now
Axel Poigne and I have agreed to write a joint paper about them.

Does anybody out there know of other papers containing such results,
or have any pet results of their own along these lines?  I mean the
kind of observation which does not merit a paper of its own but ought
to be written down somewhere. Acknowledgement or joint authorship offered.

Paul Taylor, Dept of Computing, Imperial College, London SW7 2BZ, UK
+441 589 5111 x 4980        pt@doc.ic.ac.uk

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