From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4327 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: The internal logic of a topos Date: Sun, 16 Mar 2008 23:36:28 -0700 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019874 12772 80.91.229.2 (29 Apr 2009 15:44:34 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:44:34 +0000 (UTC) To: categories list Original-X-From: rrosebru@mta.ca Mon Mar 17 10:43:32 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 Mar 2008 10:43:32 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1JbFSk-0004pC-22 for categories-list@mta.ca; Mon, 17 Mar 2008 10:33:14 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 91 Original-Lines: 17 Xref: news.gmane.org gmane.science.mathematics.categories:4327 Archived-At: As I understand the internal logic of a topos it consists of certain morphisms from finite powers of Omega to Omega. In the case of Set it consists of all such morphisms. For which toposes is this not the case, and for those how are the morphisms that do belong to the internal logic best characterized? I do hope it's not necessary to start from the notion of an internal Heyting algebra, that sounds so counter to mathematical practice and intuition. If the internal logic consists of precisely those morphisms preserved by geometric morphisms this will give me the necessary motivation to go to the mats with geometry. Vaughan