Counting models in universal Horn
John T. Baldwin, Ralph McKenzie · 1982
Define nx(h) to be either to, or the number of non-isomorphic models in ~ having cardinality h, whichever cardinal is larger. This paper contains a proof that for a congruence modular variety 7; of algebras of countable similarity type, there are only six possible functions n~-. It is also proved that if nx(h)7~2 x for some ~t, and 5g is a universal Horn class of models for a countable language, then N must satisfy two conditions, one of which is quite restrictive and requires that the members of Yt are all in a certain sense Abelian.