From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3380 Path: news.gmane.org!not-for-mail From: "Jon Cohen" Newsgroups: gmane.science.mathematics.categories Subject: Re: Laws Date: Wed, 9 Aug 2006 09:31:48 +1000 (EST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019270 8510 80.91.229.2 (29 Apr 2009 15:34:30 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:34:30 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Aug 9 17:32:36 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 09 Aug 2006 17:32:36 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GAucT-0001zF-S0 for categories-list@mta.ca; Wed, 09 Aug 2006 17:25:37 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 13 Original-Lines: 26 Xref: news.gmane.org gmane.science.mathematics.categories:3380 Archived-At: Hi, > If you want to consider the class of algebras (in general smaller than > V(Th(G))) that satisfy all the Horn clauses that G satisfies, then you > have to drop the homomorphic images. I believe that the algebras in > question will be precisely the subalgebras of products of G, but > someone might correct me if I remember this wrongly. Isomorphic images of subalgebras of products and ultraproducts, I believe - the standard notation for this seems to be $ISP_U$. Further, there is the interesting result that TH(G) =3D Th(H) for any fre= e nonabelian groups G and H. The following paper gives a summary of this result and a discussion of equations in free groups: http://www.math.mcgill.ca/olga/V00228H7.pdf best, Jon -- http://rsise.anu.edu.au/~jon