abstract: In 2003, Pillay and Ziegler reproved the function field case of Mordell-Lang in all characteristics inspired by Hrushovski's original proof but avoiding the use of the so-called Zariski Geometries. Instead, motivated on Campana's work on algebraic coreductions, they showed that given an (irreducible) definable set X of bounded differential degree in a universal differential closed field, the field of definition of the constructible set determined by X can be understood (i.e. it is internal) over a generic realisation of X in terms of a finite set of elements coming from the constant field. In model-theoretical terms, DCF_0 has the CBP for types of finite Morley rank with respect to the type of the constants. The CBP is a generalisation of 1-basedness, which has many structural consequences for the definability of groups and fields, in particular, every definable group in a 1-based theory is virtualy abelian. Another possible generalisation of 1-basedness is called CM-triviality, which prohibits the existence of a particular point-line-plane configuration, present in Euclidean Geometry. In particular, a CM-trivial theory has no infinite definable fields and in the finite rank context, all definable groups are virtually nilpotent. We will present an overview of the aforementioned concepts and present some variants of CM-triviality and discuss definability of fields and groups in this context