Logic Seminar
Krzysztof Krupinski
UIUC
Getting fields in rosy theories
Abstract: I will talk about some results yielding infinite interpretable fields in rosy groups of finite thorn U-rank. These results generalize some theorems from the finite Morley rank case and from o-minimal structures. I will prove the existence of such fields in the presence of certain V-definable rings (generalizing a result by Peterzil and Starchenko for o-minimal structures) and in a situation when an infinite, definable abelian group acts definably as a group of automorphisms on a definable abelian group. The interesting fact is that the lack of most of the tools (such as the uniform chain condition on intersections of uniformly definable subgroups or Zilber's Indecomposables theorem) has forced me to use completely fundamental tools (such as the compactness theorem and basic properties of dimension), and as a result I have obtained simpler proofs than those in the finite Morley rank case or o-minimal structures. Using these results, I have proved the existence of an infinite interpretable field in any solvable-by-finite but not nilpotent-by-finite group of finite thorn U-rank satisfying NIP.
tea at 4, talk shortly thereafter.
Monday April 28, 2008 at 4:00 PM in SEO 427