Zariski Geometries
Geometry from the Logician's Point of View

Methods and results from the theory of Zariski structures, and their applications in geometry.

Boris Zilber (Author)

9780521735605, Cambridge University Press

Paperback, published 4 February 2010

224 pages, 50 exercises
22.7 x 15.2 x 1.2 cm, 0.33 kg

'With a combination of hard mathematics and profound insights, the book makes a compelling case for the study of Zariski geometries and is highly recommended.' David Evans, Bulletin of the London Mathematical Society

This book presents methods and results from the theory of Zariski structures and discusses their applications in geometry as well as various other mathematical fields. Its logical approach helps us understand why algebraic geometry is so fundamental throughout mathematics and why the extension to noncommutative geometry, which has been forced by recent developments in quantum physics, is both natural and necessary. Beginning with a crash course in model theory, this book will suit not only model theorists but also readers with a more classical geometric background.

1. Introduction
2. Topological structures
3. Noetherian Zariski structures
4. Classification results
5. Non-classical Zariski geometries
6. Analytic Zariski geometries
A. Basic model theory
B. Geometric stability theory
References
Index.

Subject Areas: Geometry [PBM], Mathematical logic [PBCD]