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From: Dusko Pavlovic <dusko@kestrel.edu>
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Subject: Re:  Cauchy completeness of Cauchy reals
Date: Fri, 24 Jan 2003 18:21:00 -0800
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>
>
>Set. Do you think your construction works in any topos?
>
the coalgebraic structures are defined using just arithmetic. in the
first one, there is the "no infinite sequences of 1s" condition, which i
am reminded depends on markov's principle; but that is just used in the
explanation. i don't think there are other constraints.

>If so, what
>would "Cauchy reals" mean precisely in this general context?
>
it means fundamental sequence, with the equivalence relation in the
"lazy" mode, a la bishop, as described in andrej bauer's message.

if my last night's posting makes sense, then these constructivist cauchy
reals make a whole lot of difference, because they really let you avoid
the choice and get limits.

-- dusko