From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6532 Path: news.gmane.org!not-for-mail From: Gaucher Philippe Newsgroups: gmane.science.mathematics.categories Subject: what happens when a basic sentence is added ? Date: Thu, 10 Feb 2011 11:59:48 +0100 Message-ID: Reply-To: Gaucher Philippe NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: Text/Plain; charset="us-ascii" Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1297394353 24911 80.91.229.12 (11 Feb 2011 03:19:13 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 11 Feb 2011 03:19:13 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Fri Feb 11 04:19:09 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PnjXI-0003KL-VW for gsmc-categories@m.gmane.org; Fri, 11 Feb 2011 04:19:09 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:52536) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PnjXA-0003RJ-4F; Thu, 10 Feb 2011 23:19:00 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PnjX5-0005HW-0M for categories-list@mlist.mta.ca; Thu, 10 Feb 2011 23:18:55 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6532 Archived-At: Dear categorists, I have a question which is probably obvious except for me... Take a limit theory T. Add a basic sentence to this theory to obtain a theory T'. So Mod(T') is accessible, Mod(T) is locally presentable. Is Mod(T') accessibly- embedded, i.e. does Mod(T')\subset Mod(T) preserve filtered colimits for a big enough regular cardinal ? Or in other terms, what is going on when a basic axiom is added. I cannot find any answer in Adamek&Rosicky's book. Of course I ask you the question because this is my situation. In my situation T and T' are purely relational and the signature contains the same four relation symbols. The only difference between T and T' is an additional axiom which is a basic sentence. thanks in advance. pg. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]