Geometry of *-Finite Types

Abstract

AbstractAssume T is a superstable theory with < 2ℵ0 countable models. We prove that any *- algebraic type of -rank > 0 is m-nonorthogonal to a *-algebraic type of -rank 1. We study the geometry induced by m-dependence on a *-algebraic type p* of -rank 1. We prove that after some localization this geometry becomes projective over a division ring . Associated with p* is a meager type p. We prove that p is determined by p* up to nonorthogonality and that underlies also the geometry induced by forking dependence on any stationarization of p. Also we study some *-algebraic *-groups of -rank 1 and prove that any *-algebraic *-group of -rank 1 is abelian-by-finite.