Positive definability patterns

We reformulate Hrushovski's definability patterns from the setting of first order logic to the setting of positive logic. Given an h-universal theory T we put two structures on the type spaces of models of T in two languages, L and L_π. It turns out that for sufficiently saturated models, the corresponding h-universal theories T and T_π are independent of the model. We show that there is a canonical model J of T, and in many interesting cases there is an analogous canonical model J_π of T_π, both of which embed into every type space. We discuss the properties of these canonical models, called cores, and give some concrete examples.