From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7854 Path: news.gmane.org!not-for-mail From: Edmund Robinson Newsgroups: gmane.science.mathematics.categories Subject: Re: A category internal to itself Date: Thu, 5 Sep 2013 09:27:13 +0100 Message-ID: References: Reply-To: Edmund Robinson NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v1283) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1378385863 14492 80.91.229.3 (5 Sep 2013 12:57:43 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 5 Sep 2013 12:57:43 +0000 (UTC) Cc: categories list To: Andrej Bauer Original-X-From: majordomo@mlist.mta.ca Thu Sep 05 14:57:46 2013 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1VHZ83-00056R-Lp for gsmc-categories@m.gmane.org; Thu, 05 Sep 2013 14:57:43 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:36135) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1VHZ6x-0008IK-Tf; Thu, 05 Sep 2013 09:56:35 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1VHZ6w-0003XT-Sx for categories-list@mlist.mta.ca; Thu, 05 Sep 2013 09:56:34 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7854 Archived-At: There are some forms of set theory in which there are restrictions on = the forms of comprehension allowed, and as a result there is a set of = all sets. Quine's New Foundations is one of these. It has a simple = restriction on the forms of predicates allowed in comprehensions. Put = simply this is that you can assign (integer) levels to the variables in = the formula so that x e y only occurs when y is at the level immediately = above x. This means that in models of this set theory there is also an = internal category of all sets.=20 best Edmund On 4 Sep 2013, at 10:23, Andrej Bauer wrote: > Chatting at a conference, the question came up why there is no > (non-trivial) category which is "internal to itself" (interpret this > in some sensible sense). And over coffee we thought this must be well > known, but not to us. Can somene shed some light on the matter? >=20 > With kind regards, >=20 > Andrej >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]