From: Dusko Pavlovic <dusko@kestrel.edu>
To: CATEGORIES LIST <categories@mta.ca>
Subject: Re: Cauchy completeness of Cauchy reals
Date: Fri, 24 Jan 2003 18:21:00 -0800 [thread overview]
Message-ID: <3E31F48C.90308@kestrel.edu> (raw)
In-Reply-To: <15920.65167.864071.575967@acws-0054.cs.bham.ac.uk>
>
>
>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
next prev parent reply other threads:[~2003-01-25 2:21 UTC|newest]
Thread overview: 27+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-01-15 14:00 Generalization of Browder's F.P. Theorem? Peter McBurney
2003-01-16 14:04 ` Steven J Vickers
2003-01-16 23:00 ` Prof. Peter Johnstone
2003-01-16 23:05 ` Michael Barr
2003-01-21 18:11 ` Andrej Bauer
2003-01-22 10:13 ` Cauchy completeness of Cauchy reals Martin Escardo
2003-01-22 23:33 ` Dusko Pavlovic
2003-01-23 19:56 ` Category Theory in Biology Peter McBurney
2003-01-24 8:51 ` Cauchy completeness of Cauchy reals Martin Escardo
2003-01-25 2:21 ` Dusko Pavlovic [this message]
2003-01-25 16:24 ` Prof. Peter Johnstone
2003-01-27 3:57 ` Alex Simpson
2003-01-23 6:29 ` Vaughan Pratt
2003-02-04 0:47 ` Vaughan Pratt
2003-02-05 16:06 ` Prof. Peter Johnstone
2003-01-23 9:50 ` Mamuka Jibladze
2003-01-24 1:34 ` Ross Street
2003-01-24 16:56 ` Dusko Pavlovic
2003-01-24 19:48 ` Dusko Pavlovic
2003-01-27 17:41 Andrej Bauer
2003-01-28 1:50 ` Alex Simpson
2003-01-28 9:44 Andrej Bauer
2003-01-28 20:51 Dusko Pavlovic
2003-01-29 2:00 ` Toby Bartels
2003-01-29 8:35 ` Alex Simpson
2003-02-04 9:15 ` Dusko Pavlovic
2003-02-05 20:56 ` Toby Bartels
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=3E31F48C.90308@kestrel.edu \
--to=dusko@kestrel.edu \
--cc=categories@mta.ca \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).