Stable Domination and Independence in Algebraically Closed Valued Fields

Deirdre Haskell, Ehud Hrushovski, Dugald Macpherson (Autoren)

Buch | Hardcover

194 Seiten

2007
Cambridge University Press (Verlag)
978-0-521-88981-0 (ISBN)

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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.

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.

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.

Erscheint lt. Verlag	10.12.2007
Reihe/Serie	Lecture Notes in Logic
Verlagsort	Cambridge
Sprache	englisch
Maße	157 x 235 mm
Gewicht	440 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	0-521-88981-2 / 0521889812
ISBN-13	978-0-521-88981-0 / 9780521889810
Zustand	Neuware