This is a short survey of some work of the author and her collaborators applying ideas of stability theory, viz. independence of types, in the context of valued fields. This work has now appeared in book form [D. Haskell, E. Hrushovski and H. D. Macpherson, Stable domination and independence in algebraically closed valued fields. Cambridge: Cambridge University Press. Lecture Notes in Logic 30 (2008; Zbl 1149.03027)]. Over the last twenty five years, ideas of stability theory have constantly penetrated applied model theory and are currently a main driving force in the mainstream of the subject. In particular, these ideas have migrated successfully to non-stable contexts. The best example is perhaps the concept of o-minimality, a landmark on the applied side being Wilkie’s proof of the model-completeness of the reals with exponentiation. The work being surveyed lays some fundamentals for applications in valued fields, valuations being fundamental objects in number theory and algebraic geometry. The survey is carefully written, with well-chosen and informative examples.
For the entire collection see [Zbl 1131.03001].