From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9906 Path: news.gmane.org!.POSTED.blaine.gmane.org!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Arithmetisation dans le topos Date: Thu, 9 May 2019 16:59:57 +0930 Message-ID: Reply-To: David Roberts Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Injection-Info: blaine.gmane.org; posting-host="blaine.gmane.org:195.159.176.226"; logging-data="34001"; mail-complaints-to="usenet@blaine.gmane.org" To: "categories@mta.ca list" Original-X-From: majordomo@mlist.mta.ca Thu May 09 21:11:08 2019 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.55]) by blaine.gmane.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.89) (envelope-from ) id 1hOoRf-0008ha-Ep for gsmc-categories@m.gmane.org; Thu, 09 May 2019 21:11:07 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46627) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1hOoSq-0002zV-6g; Thu, 09 May 2019 16:12:20 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1hOoQU-0004kF-80 for categories-list@mlist.mta.ca; Thu, 09 May 2019 16:09:54 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9906 Archived-At: Dear all, some years back I put out a call for any information about Joyal's lecture(s) containing his arithmetic universe proof of G=C3=B6del's incompleteness theorem. It was suggested I ask Anders Kock, and he was able to give me if not that lecture, but a related lecture from 1974, with the above title. It contained a rough definition of an arithmetic universe, namely a pretopos in which the free category on any internal graph exists. There was also some good material on classifying toposes. For historical interest I have made the notes available, with Anders' permission, here: https://thehighergeometer.wordpress.com/2019/05/08/joyal-arithmetisation-dans-le-topos/ Others may be interested as to the state of the art at the time. I hope that one day we will see details of the incompleteness proof that still eludes my grasp! Best regards, David David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]