Zariski Geometries

Zariski Geometries : Geometry from the Logician's Point of View

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Description

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.show more

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Review quote

'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 Societyshow more

About Boris Zilber

Boris Zilber is Professor of Mathematical Logic in the Mathematical Institute at the University of Oxford.show more

Table of contents

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.show more