Stable Domination and Independence in Algebraically Closed Valued Fields
1st Edition
Published on 31. January 2008
978-0-511-36798-4 (ISBN)
Description
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.
Reviews / Votes
Review of the hardback: '... comprehensive and stimulating ...' EMS NewsletterMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
1,43 MB
ISBN-13
978-0-511-36798-4 (9780511367984)
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Schweitzer Classification
Other editions
Additional editions
Deirdre Haskell | Ehud Hrushovski | Dugald Macpherson
Stable Domination and Independence in Algebraically Closed Valued Fields
Book
06/2011
Cambridge University Press
€54.20
Shipment within 15-20 days
Deirdre Haskell | Ehud Hrushovski | Dugald Macpherson
Stable Domination and Independence in Algebraically Closed Valued Fields
Book
12/2007
Cambridge University Press
€149.70
Shipment within 15-20 days
Persons
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.
Content
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.
