Antiadditive Primitive Connected Theories

Our main goal is to prove that an infinite group is interpreted in every primitive connected non-superstable theory. Previously, we have introduced the concept of primitive connected theories, for which the quantifier elimination theorem was proved generalizing a similar elimination result for modules due to Baur, Monk, and Garavaglia. Here, we study primitive connected theories in which an infinite group is not interpreted, that is, theories that differ radically from theories of modules, but have a similar structure theory. Such are said to be antiadditive. (Note that theories of modules, as distinct from antiadditive ones, may be non-superstable.)