Re: chains vs. directed sets
Date: Tue, 26 Nov 91 13:27:08 GMT
To: "John C. Mitchell" <email@example.com>
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  or  with my paper
Homomorphisms, Bilimits & Saturated Domains - some very basic domain th.
, which was unpublished, but is available by anonymous FTP from
theory.doc.ic.ac.uk (188.8.131.52) as theory/papers/Taylor/bilimits.dvi