Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.
The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered.
This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.
Introduction 1. Elimination Over Skew Fields, P.M. Cohn 2. The Model Theory of Abelian P-Groups, P.C. Eklof 3. Non-Existence of Universals for Classes Like Reduced Torsion Free Abelian Groups Under Embeddings Which Are Not Necessarily Pure, S. Shelah 4. A Class of Potential Counter-Examples to the Pure Semisimplicity Conjecture, D. Simson