Re: chains vs. directed sets

Date: Tue, 26 Nov 91 13:27:08 GMT
To: "John C. Mitchell" <jcm@cs.stanford.edu>

The reason for using directed sets rather than chains is much the same
as the reason for using typed programming languages rather than Kleene
indices: the class of them is closed under the useful operations
(products, for instance) whereas indices involve coding which is quite
irrelevant to the problem.

For example, in the limit-colimit coincidence, compare the notation of
Smyth & Plotkin [78] or [82] with my paper
        Homomorphisms, Bilimits & Saturated Domains - some very basic domain th.
[1987], which was unpublished, but is available by anonymous FTP from
        theory.doc.ic.ac.uk  ( as theory/papers/Taylor/bilimits.dvi