Lecture Notes in Logic, 30 Stable Domination and Independence in Algebraically Closed Valued Fields   Deirdre Haskell, Ehud Hrushovski, Dugald Macpherson

This book addresses a gap in the model-theoretic understanding of valued fields that has, until now, limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part one of the book is a study of stably dominated types and it begins with an introduction to the key ideas of stability theory for stably dominated types. Part two continues with an outline of some classical results in the model theory of valued fileds and explores the application of stable domination to algebraically closed valued fileds. The research presented here is made accessible to the general model theorist by the inclusion of the introductory sections of each part.

Year: 2007
Price:$65.00 ISBN-13:9780521889810
194 pages. Hardcover.
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Table of Contents

Introduction

Part I. Stable Domination:

Chapter 2. - Some background on stability theory
Chapter 3. - Definition and baisc properties of Stc
Chapter 4. - Invariant types and change of base
Chapter 5. - A combinatorial lemma
Chapter 6. - Strong codes for germs

Part II. Independence in ACVF:

Chapter 7. - Some bacground on algebraically closed valued fields
Chapter 8. - Sequential independence
Chapter 9. - Growth of the stable part
Chapter 10. - Types orthogonal to \Gamma
Chapter 11. - Opacity and prime resolutions
Chapter 12. - Maximally complete fields and domination
Chapter 13. - Invariant types
Chapter 14. - A maximum modulus principle
Chapter 15. - Canonical bases and independence give by modules
Chapter 16. - Other Henselian fields

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