From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6731 Path: news.gmane.org!not-for-mail From: Andrej Bauer Newsgroups: gmane.science.mathematics.categories Subject: Re: size_question Date: Sat, 2 Jul 2011 14:24:03 +0200 Message-ID: References: Reply-To: Andrej Bauer NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1309631259 18872 80.91.229.12 (2 Jul 2011 18:27:39 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 2 Jul 2011 18:27:39 +0000 (UTC) Cc: Categories To: James Lipton Original-X-From: majordomo@mlist.mta.ca Sat Jul 02 20:27:35 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.30]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Qd4uk-0003ON-LD for gsmc-categories@m.gmane.org; Sat, 02 Jul 2011 20:27:34 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44843) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Qd4sa-0002rE-Gj; Sat, 02 Jul 2011 15:25:20 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qd4sZ-0005Ry-Sj for categories-list@mlist.mta.ca; Sat, 02 Jul 2011 15:25:19 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6731 Archived-At: On Wed, Jun 29, 2011 at 4:43 AM, James Lipton wrote: > These are the "hereditarily finite sets" > > =C2=A0 =C2=A0V(0) =3D empty set > > =C2=A0 V(n+1) =3D P(V(n)) > > V(omega) =3D U{V(n): n in omega} > > I would not call it "the" cat of finite sets, since there uncountably man= y > countable models of ZF. Obviously the choice of ZF, rather than say Zerme= lo > set theory or some other foundation is also pretty arbitrary. I should think that the hereditarily finite sets do not depend all that much on the background setting. After all, there are not very many of them and they are quite concrete. Can they really be hugely different depending on whether we work in ZF, ZFC, IZF, CZF etc? With kind regards, Andrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]