GEOMETRIES AND MODELS - an Introduction Spring 2012

These lecture notes give a short introduction to ideas shared by classical theory of geometries and modern model theory. This course is not on stability theory and thus all the non-trivial results from stability theory are replaced by stronger assumptions, except three: Shelah’s finite equivalence relation theorem, one consequence of splitting and the fact that ∞ -definable groups in models of ω -stable theories are definable. These three are considered as facts i.e. the proofs are skipped. Also, we try to keep all the objects studied as concrete as possible and so although our main theorem (Conclusion 11.3) is a variant of a special case of a result from [Hr], the proof follows [HLS] and [Hy] most of the time. Additional benefit of this is that most of the proofs work also in many non-elementary cases. For the history of this topic, see [Pi] and [Po].