From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5553 Path: news.gmane.org!not-for-mail From: Bas Spitters Newsgroups: gmane.science.mathematics.categories Subject: Logical consequences of descent theory Date: Wed, 3 Feb 2010 15:57:38 +0100 Message-ID: Reply-To: Bas Spitters NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: ger.gmane.org 1265220107 21004 80.91.229.12 (3 Feb 2010 18:01:47 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 3 Feb 2010 18:01:47 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Wed Feb 03 19:01:42 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1NcjXq-0004C1-5t for gsmc-categories@m.gmane.org; Wed, 03 Feb 2010 19:01:42 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Ncj8Z-0001Ea-7z for categories-list@mta.ca; Wed, 03 Feb 2010 13:35:35 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5553 Archived-At: A number of people have suggested that descent theory has been/ can be used to obtain logical results. I can sort of see the possible connections: open surjective maps between toposes are effective descent morphisms. Viewed logically, such a map is a conservative extension preserving all first-order structure. Proper surjective maps are also effective descent morphisms. Consider an occupied locale X (in Paul Taylor's sense). I.e. X->1 is a proper surjection. Then we obtain a proper surjection Sh(X)->Sets. I.e. we conservatively add a generic point of the occupied space. The inverse image preserves geometric logic, but does it preserve anything else in general? This is probably well-known, but I couldn't find it. Any suggestions or pointers about the logical interpretation of descent theory would be appreciated. Thanks, Bas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]