From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5277 Path: news.gmane.org!not-for-mail From: burroni@math.jussieu.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: to PTJ Date: Sun, 15 Nov 2009 18:20:51 +0100 Message-ID: References: Reply-To: burroni@math.jussieu.fr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1258328260 1225 80.91.229.12 (15 Nov 2009 23:37:40 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 15 Nov 2009 23:37:40 +0000 (UTC) To: "Joyal, =?iso-8859-1?b?QW5kcuk=?=" , categories@mta.ca Original-X-From: categories@mta.ca Mon Nov 16 00:37:33 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1N9oez-0007u0-19 for gsmc-categories@m.gmane.org; Mon, 16 Nov 2009 00:37:33 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1N9oHq-0003bA-9f for categories-list@mta.ca; Sun, 15 Nov 2009 19:13:38 -0400 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5277 Archived-At: Hi, You can find this equation (and ref to Higman and Neumann) in the GTM =20 springer no 26 page 7 : E.G. manes "Algebraic Theory. xxxdydzdxxdxdzddd=3Dy (polish notations and d is the binary operation.) Best, Albert "Joyal, Andr=E9" a =E9crit=A0: > Hi Peter, > >> And, as someone (I forget who, but it may have been Mike Barr) pointed >> out long ago, one can (well, almost) define the variety of groups >> as the variety defined by a single binary operation satisfying a >> single equation; 1 < 3, but no sane group-theorist would do it >> that way. > > I recall that Tarski is responsible for describing > the theory of groups with a single binary operation satisfying a > single equation. But dont have a reference with me. > > A small point: the algebraic theory described by Tarski > admits the empty set as a model. Strictly speaking, > it is not equivalent to the theory of group. > > Best, > Andr=E9 > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]