From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2120 Path: news.gmane.org!not-for-mail From: Martin Escardo Newsgroups: gmane.science.mathematics.categories Subject: Re: Cauchy completeness of Cauchy reals Date: Fri, 24 Jan 2003 08:51:27 +0000 Message-ID: <15920.65167.864071.575967@acws-0054.cs.bham.ac.uk> References: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII X-Trace: ger.gmane.org 1241018424 2578 80.91.229.2 (29 Apr 2009 15:20:24 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:20:24 +0000 (UTC) To: CATEGORIES LIST Original-X-From: rrosebru@mta.ca Fri Jan 24 13:47:09 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 24 Jan 2003 13:47:09 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18c7u7-00047g-00 for categories-list@mta.ca; Fri, 24 Jan 2003 13:46:11 -0400 In-Reply-To: X-Mailer: VM 6.89 under 21.1 (patch 14) "Cuyahoga Valley" XEmacs Lucid Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 45 Original-Lines: 18 Xref: news.gmane.org gmane.science.mathematics.categories:2120 Archived-At: Dusko Pavlovic writes: > >NB. Freyd characterized the Dedekind reals as a final coalgebra. Alex > >Simpson and I characterized "the Cauchy completion of the rationals > >within the Dedekind reals" as a free algebra > > > and vaughan pratt and i characterized the cauchy reals as a final > coalgebra. the papers are i proceedings of CMCS 99 and in TCS 280. I forgot to mention this --- I apologize. In your paper, you work in Set. Do you think your construction works in any topos? If so, what would "Cauchy reals" mean precisely in this general context? Thanks. ME