From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9507 Path: news.gmane.org!.POSTED!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: does countable choice survive booleanization? Date: Fri, 19 Jan 2018 15:36:17 +0100 Message-ID: References: Reply-To: Thomas Streicher NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: blaine.gmane.org 1516408205 28512 195.159.176.226 (20 Jan 2018 00:30:05 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sat, 20 Jan 2018 00:30:05 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sat Jan 20 01:30:01 2018 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1ech2Q-0005mk-9o for gsmc-categories@m.gmane.org; Sat, 20 Jan 2018 01:29:38 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:59849) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1ech5D-0006DC-D6; Fri, 19 Jan 2018 20:32:31 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ech3w-0001fH-UQ for categories-list@mlist.mta.ca; Fri, 19 Jan 2018 20:31:12 -0400 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9507 Archived-At: Alex Simpson has just told me that the answer to my question is simple: all presheaf toposes validate ICC but certainly not all their booleanizations since there are many boolean Groth. toposes not validating ICC. Thank you Alex! Alas, this doesn't answer the question for booleanizations of generalized relative realizability toposes as e.g. the Kleene Vesley topos. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]