From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4097 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: when are Lindenbaum-Tarski algebras complete? Date: Wed, 21 Nov 2007 15:33:32 +0100 (CET) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019717 11693 80.91.229.2 (29 Apr 2009 15:41:57 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:41:57 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Nov 21 16:42:56 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 Nov 2007 16:42:56 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IuwBs-0006mx-Kw for categories-list@mta.ca; Wed, 21 Nov 2007 16:28:56 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 51 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:4097 Archived-At: I also suspect that Sub(1) of the free topos with nno is not complete. But countability does not suffice for refuting completeness (the ordinal \omega + 1 is an infinite countable cHa which nevertheless is complete). >>From Goedel's Theorem for HAH (higher order intuit. arithmetic) it follows that Sub(1) of the free topos with nno is not atomic. But that also doesn't suffice for refuting completeness. On p.169 of Freyd, Friedman and Scedrov's paper "Lindenbaum algebras of intuitionistic theories and free categories" (APAL 35) they claim "Lindenbaum algebras are almost never complete" but don't give a proof. Thomas Streicher