Abstract

Bounded PAC substructures of models of stable theory T are generalizations of bounded PAC fields and bounded PAC beautiful pairs generalize Poizat's beautiful pairs. Both notions were introduced in the authors Ph.D. thesis. In this paper, we prove that under the assumption that the PAC property is first order for T, the theory of any bounded PAC structure is simple. Moreover, if the PAC property is first order for T and T does not have the finite cover property, then the theory of any bounded PAC beautiful pair is simple. We, also, give a characterization of dividing in both cases.