Stable Domination and Independence in Algebraically Closed Valued Fields

by Deirdre Haskell, Ehud Hrushovski, Dugald Macpherson

Overview

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 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.

Product Details

ISBN-13:	9780521335157
Publisher:	Cambridge University Press
Publication date:	06/30/2011
Series:	Lecture Notes in Logic , #30
Pages:	196
Product dimensions:	5.90(w) x 9.00(h) x 0.60(d)

About the Author

Deirdre Haskell is a Professor in the Department of Mathematics and Statistics at McMaster University.

Ehud Hrushovski is a Professor in the School of Mathematics at the University of Leeds.

Dugald Macpherson is a Professor in the Department of Mathematics at the Hebrew University at Jerusalem.

Table of Contents

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 Γ; 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.

Editorial Reviews

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

From the Publisher