From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6535 Path: news.gmane.org!not-for-mail From: Jiri Adamek Newsgroups: gmane.science.mathematics.categories Subject: Re: what happens when a basic sentence is added ? Date: Fri, 11 Feb 2011 17:36:04 +0100 (CET) Message-ID: References: Reply-To: Jiri Adamek NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1297455219 4435 80.91.229.12 (11 Feb 2011 20:13:39 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 11 Feb 2011 20:13:39 +0000 (UTC) Cc: categories@mta.ca To: Gaucher Philippe Original-X-From: majordomo@mlist.mta.ca Fri Feb 11 21:13:32 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 1PnzMr-0002xG-Vi for gsmc-categories@m.gmane.org; Fri, 11 Feb 2011 21:13:26 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:43602) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PnzMX-0000j4-Oq; Fri, 11 Feb 2011 16:13:05 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PnzMS-0008RJ-08 for categories-list@mlist.mta.ca; Fri, 11 Feb 2011 16:13:00 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6535 Archived-At: Dear Philippe, Your question about limit theories 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 has an affirmative answer, essentailly due to Coste's 1979 paper. Take a cardinal k larger than the arities of the symbols of your signature S, then both Mod(T) and Mod(T') are closed under k-filtered colimits in Str S. (See the ananlogous argument in part II of the proof of Theroem 5.9 of Rosicky's and mine book.) Consequently, the embedding Mod(T') -> Mod(T) preserves k-filtered colimits. Best regards Jiri [For admin and other information see: http://www.mta.ca/~cat-dist/ ]