On two hierarchies of dimensions

Abstract

AbstractLet T be a countable, complete, ω-stable, nonmultidimensional theory. By Lascar [7], in Teq there is in every dimension of T a type with Lascar rank ωα for some α. We give sufficient conditions for α to coincide with the level of that dimension in Pillay's [10] RK-hierarchy of dimensions computed in Teq. In particular, this is fulfilled for modules.