Hyperfinite MV-algebras

In this paper, we will be concerned with Hyperfinite MV-algebras, which are infinite models of the theory of finite MV-algebras. We have three main results. As a first main result, we show that every hyperfinite MV-algebra is elementarily equivalent to a product of finite or hyperfinite MV-chains. As a second main result, we give an explicit, recursive axiomatization of finite or hyperfinite MV-algebras; this implies the decidability of the theory of all finite MV-algebras. As a third main result, we show that if A is a hyperfinite MV-algebra, then A/Rad(A) is infinite.