From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2261 Path: news.gmane.org!not-for-mail From: Peter Freyd Newsgroups: gmane.science.mathematics.categories Subject: correction Date: Mon, 28 Apr 2003 12:12:45 -0400 (EDT) Message-ID: <200304281612.h3SGCjjT028244@saul.cis.upenn.edu> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241018533 3295 80.91.229.2 (29 Apr 2009 15:22:13 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:22:13 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Apr 28 19:46:57 2003 -0300 X-Keywords: Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 28 Apr 2003 19:46:57 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19AHLD-0005rN-00 for categories-list@mta.ca; Mon, 28 Apr 2003 19:43:19 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:2261 Archived-At: Vaughan has noticed that I hadn't broken the commutative habit. So let me start again. He asked if one can determine a minimal equational theory with the theory of distributive lattices as its unique maximal consistent extension. Yes, here's an example: x meet 1 = x, x meet 0 = 0, 1 join 1 = 1, 1 join 0 = 1, 0 join 1 = 1, 0 join 0 = 0. (I was missing the penultimate equation.) There is a Klein-group's worth of variations. One operation simultaneously interchanges meet and join, 0 and 1. Another operation simultaneously interchanges the arguments of the operators. I'll hazard that the resulting four theories are the only ones that do the trick.