Model Theory, Algebra, and Geometry

Erscheinungsjahr 2013
ISBN: 978-0-521-78068-1
Verlag: Cambridge University Press

Buch, Englisch, Band 39, 256 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 523 g

Reihe: Mathematical Sciences Research Institute Publications

Model theory has, in recent years, made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications range from a proof of the rationality of certain Poincare series associated to varieties over p-adic fields, to a proof of the Mordell-Lang conjecture for function fields in positive characteristic. In some cases (such as the latter) it is the most abstract aspects of model theory which are relevant. This book, arising from a series of introductory lectures for graduate students, provides the necessary background to understanding both the model theory and the mathematics behind these applications. The book is unique in that the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations) is covered and diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) are introduced and discussed, all by leading experts in their fields.

Autoren/Hrsg.

Haskell, Deidre

Pillay, Anand

Steinhorn, Charles

Haskell, Deirdre

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

1. Introduction to model theory David Marker; 2. Some classical model theory of fields Lou van den Dries; 3. Introduction to the model theory of differential fields David Marker; 4. Notes on o-minimality and variations Dugald Macpherson; 5. A survey on the model theory of difference fields Zoe Chatzidakis; 6. Dimension theory Bradd Hart; 7. Model theory and the Mordell-Lang conjecture Barry Mazur; 8. Semialgebraic and subanalytic geometry Edward Bierstone; 9. Model theory and geometry Jan Denef.