8 Aug
2006
8 Aug
'06
11:31 p.m.
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) = Th(H) for any free 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