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Re: chains vs. directed sets
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Subject: Re: chains vs. directed sets
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From: val@saul.cis.upenn.edu (Val Breazu-Tannen)
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Date: Tue, 26 Nov 91 21:51:51 EST
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Cc: types
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In-Reply-To: John C. Mitchell's message of Mon, 25 Nov 91 19:24:11 EST <199111260024.AA18568@stork.lcs.mit.edu>
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Sender: meyer@theory.lcs.mit.edu
Date: Tue, 26 Nov 91 19:29:47 EST
To: jcm@cs.stanford.edu
Apparently, Iwamura was the first to show (1944) that chain-complete
implies directed-complete. The result is mentioned in Cohn's book on
universal algebra. Iwamura's result was sharpened by Markowski (Alg
Univ 6, 1976, 53-68) who also shows that chain-continuous implies
directed-continuous. (I think this is the paper Curien alludes to).
The omega-algebraicity conditions used by Plotkin and Zhang are
superfluous.
Val Tannen