From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2223 Path: news.gmane.org!not-for-mail From: "C.F.Townsend" Newsgroups: gmane.science.mathematics.categories Subject: Prime Ideal Theorem implies Excluded Middle? Date: Sat, 22 Mar 2003 14:39:08 -0000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" X-Trace: ger.gmane.org 1241018507 3121 80.91.229.2 (29 Apr 2009 15:21:47 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:21:47 +0000 (UTC) To: "'categories@mta.ca'" Original-X-From: rrosebru@mta.ca Sat Mar 22 16:28:39 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 22 Mar 2003 16:28:39 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18wpUl-0002f7-00 for categories-list@mta.ca; Sat, 22 Mar 2003 16:21:35 -0400 X-Mailer: Internet Mail Service (5.5.2448.0) Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 13 Original-Lines: 17 Xref: news.gmane.org gmane.science.mathematics.categories:2223 Archived-At: Dear all, does anyone know a reference for the question: Prime Ideal Theorem implies the Excluded Middle ? Certainly, Axiom of Choice implies Excluded Middle, but I have convinced myself that the weaker statement is true and would be grateful for any pointers. Regards, Christopher Townsend PS there are definitely formulations of the PIT that do not use negation. E.g. it is equivalent to the statement that for every Boolean alg. B if x in B has the property that f(x)=0 for every Boolean alg. homomorphism f:B->Omega, then x=0.