From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5246 Path: news.gmane.org!not-for-mail From: Andrej Bauer Newsgroups: gmane.science.mathematics.categories Subject: Re: intersections of classes Date: Thu, 12 Nov 2009 07:28:16 +0100 Message-ID: References: Reply-To: Andrej Bauer NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1258047198 21175 80.91.229.12 (12 Nov 2009 17:33:18 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 12 Nov 2009 17:33:18 +0000 (UTC) To: Andrew Salch , categories@mta.ca Original-X-From: categories@mta.ca Thu Nov 12 18:33:12 2009 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 4.50) id 1N8dXj-0004P0-96 for gsmc-categories@m.gmane.org; Thu, 12 Nov 2009 18:33:11 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1N8cwC-0007g1-2L for categories-list@mta.ca; Thu, 12 Nov 2009 12:54:24 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5246 Archived-At: On Wed, Nov 11, 2009 at 10:36 PM, Andrew Salch wrote: > I have a question for the category theorists which is unfortunately just > an issue about sets and classes that I hope some of you have thought about > before, and can help me with: let C be a class, and consider a family of > subclasses C_i of C, which are indexed by an index class I. Am I allowed > to take the intersection of a family of classes indexed by a class? Is the > result a class? Suppose the class I is described by a first-order formula a(x) and the classes C_i are described by a first-order formula c(x,i), i.e: I = {i | a(i)} C_i = {x | c(x,i)} Then the intersection of the C_i's is a class because it is described as D = {x | forall i, a(i) => c(x,i)} Your condition that the C_i's are contained in a class C is redundant because we may always take C=V, the universe. With kind regards, Andrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]