2009 seminar talk: Two aspects of stability theory
Talk held by Hans Adler (University of Leeds) at the KGRC seminar on 2009-01-15.
Stability theory as practised by Shelah has a set theoretic flavour. It uses methods of infinite combinatorics to get results that often vary with the model of ZFC. Mainstream stability theory is much more geometric in character, and Hrushovski's group construction is analogous to a famous lattice theoretic theorem of von Neumann. The distinction becomes more important now that we are moving to more general contexts. Dependent (NIP) theories and rosy theories both generalise stable theories. The former have most of the combinatorial properties of stable theories, while the latter preserve most of the geometric properties.