Stable Domination and Independence in Algebraically Closed Valued Fields

This book presents research in model theory and its applications to valued fields.

Deirdre Haskell (Author), Ehud Hrushovski (Author), Dugald Macpherson (Author)

9780521335157, Cambridge University Press

Paperback, published 30 June 2011

196 pages
22.9 x 15 x 1.8 cm, 0.3 kg

Review of the hardback: '… comprehensive and stimulating …' EMS Newsletter

This book addresses a gap in the model-theoretic understanding of valued fields that had limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part I of the book is a study of stably dominated types. These form a subset of the type space of a theory that behaves in many ways like the space of types in a stable theory. This part begins with an introduction to the key ideas of stability theory for stably dominated types. Part II continues with an outline of some classical results in the model theory of valued fields and explores the application of stable domination to algebraically closed valued fields. The research presented here is made accessible to the general model theorist by the inclusion of the introductory sections of each part.

1. Introduction
Part I. Stable Domination: 2. Some background on stability theory
3. Definition and basic properties of Stc
4. Invariant types and change of base
5. A combinatorial lemma
6. Strong codes for germs
Part II. Independence in ACVF: 7. Some background on algebraically closed valued fields
8. Sequential independence
9. Growth of the stable part
10. Types orthogonal to ?
11. Opacity and prime resolutions
12. Maximally complete fields and domination
13. Invariant types
14. A maximum modulus principle
15. Canonical bases and independence given by modules
16. Other Henselian fields.

Subject Areas: Algebra [PBF], Mathematical logic [PBCD]