Forking in pregeometries.

Abstract: "The aim of this paper is to set the foundation to separate geometric model theory from model theory. Our thesis is that it is possible to lift results from geometric model theory to non first order logic (e.g. L[subscript omegaΓéü, omega]). We introduce a relation between subsets of a pregeometry and show that it satisfies all the formal properties that forking satisfies in simple first order theories. This is important when one is trying to lift forking to nonelementary classes, in contexts where there exists pregeometries but not necessarily a well-behaved dependence relation (see for example [HySh]). We use these to reproduce S. Buechler's characterization of local modularity in general. These results are used by Lessmann to prove an abstract group configuration theorem in [Le2]."