AssumeTis a superstable theory with 0 is m-nonorthogonal to a *-algebraic type of-rank 1. We study the geometry induced by m-dependence on a *-algebraic typep*of-rank 1. We prove that after some localization this geometry becomes projective over a division ring. Associated withp*is a meager typep. We prove thatpis determined byp*up to nonorthogonality and thatunderlies also the geometry induced by forking dependence on any stationarization ofp. Also we study some *-algebraic *-groups of-rank 1 and prove that any *-algebraic *-group of-rank 1 (...) is abelian-by-finite. (shrink)

Assume T is a small superstable theory. We introduce the notion of a flat Morley sequence, which is a counterpart of the notion of an infinite Morley sequence in a type p, in case when p is a complete type over a finite set of parameters. We show that for any flat Morley sequence Q there is a model M of T which is τ-atomic over {Q}. When additionally T has few countable models and is 1-based, we prove that within (...) M there is an infinite Morley sequence I, with I $\subset$ dcl(Q), such that M is prime over I. (shrink)

We investigate some topological properties of the spaces of classes of bounded type-definable equivalence relations.

We investigate profinite structures in the sense of Newelski interpretable in fields. We show that profinite structures interpretable in separably closed fields are the same as profinite structures weakly interpretable in . We also find a strong connection with the inverse Galois problem. We give field theoretic constructions of profinite structures weakly interpretable in and satisfying some model theoretic properties, like smallness, m-normality, non-triviality, being -rank 1. For example we interpret in this way the profinite structure consisting of the profinite (...) group together with a distinguished Sylow p-subgroup of its standard structural group. (shrink)

LetTbe a countable, small simple theory. In this paper, we prove that for suchT, the notion of Lascar strong type coincides with the notion of strong type, over an arbitrary set.

Let T be a countable, small simple theory. In this paper, we prove that for such T, the notion of Lascar strong type coincides with the notion of strong type, over an arbitrary set.

We study the groups Gal L and Gal KP, and the associated equivalence relations EL and EKP, attached to a first order theory T. An example is given where EL≠ EKP. It is proved that EKP is the composition of EL and the closure of EL. Other examples are given showing this is best possible.

We propose a model-theoretic framework for investigating profinite groups. Within this framework we define and investigate small profinite groups. We consider the question if any small profinite group has an open abelian subgroup.