From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6790 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: size_question_encore Date: Fri, 15 Jul 2011 09:51:49 -0700 Message-ID: <20110715165149.GA22765@ugcs.caltech.edu> References: Reply-To: Toby Bartels NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: dough.gmane.org 1310824757 13036 80.91.229.12 (16 Jul 2011 13:59:17 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 16 Jul 2011 13:59:17 +0000 (UTC) To: Categories Original-X-From: majordomo@mlist.mta.ca Sat Jul 16 15:59:10 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Qi5Oe-00039r-Jo for gsmc-categories@m.gmane.org; Sat, 16 Jul 2011 15:59:08 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:54212) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1Qi5Mc-0002D8-8J; Sat, 16 Jul 2011 10:57:02 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qi5Mb-00077f-IZ for categories-list@mlist.mta.ca; Sat, 16 Jul 2011 10:57:01 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6790 Archived-At: Michael Shulman wrote in part: >We can make finitely many choices without any axiom of >choice. Thus, for any natural number n, by applying collection n >times, we can find *some* n^th iterate of the "construction". >(Formally, we prove this by induction on n.) Applying the axiom of >collection again over the natural numbers, we obtain a set which >contains at least one n^th iterate of the "construction" for every >natural number n. Taking the union of this set, we should obtain a >set of objects whose corresponding full subcategory contains at least >one limit of every finite diagram therein. OK, I buy that. The part where we take the union is the step that doesn't generalise to arbitrary applications of DC. --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]