This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
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In this informal presentation we introduce some of the main definitions and results which form the basis of model theory. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof of the Claim, Model Theory of Fields, Inventiones Math, New York, Oxford University Press, Serge Lang, The Model Theory of Groups, American Journal of Math, Geometrical Stability Theory, Notre Dame University Press, Symbolic Logic, Annals of Math, Proof of Manin New!
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In this informal presentation we introduce some of the main definitions and results which form the basis of model theory. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof of the Claim, Model Theory of Fields, Inventiones Math, New York, Oxford University Press, Serge Lang, The Model Theory of Groups, American Journal of Math, Geometrical Stability Theory, Notre Dame University Press, Symbolic Logic, Annals of Math, Proof of Manin New!
Books on Related Topics Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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- Model Theory of Fields: Lecture Notes in Logic 5, Second Edition by David Marker on 5 pages
- Number Theory III: Diophantine Geometry (Encyclopaedia of Mathematical Sciences) by Serge Lang on page 99, page 106, and page 205
- Model Theory of Groups (Notre Dame Mathematical Lectures) by Ali Nesin on page 59, page 83, and page 127
- Basic algebraic geometry (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berucksichtigung der Anwendungsgebiete) by I. R Shafarevich on page 84, page 100, and page 128
- Algebraic Groups and Class Fields (Graduate Texts in Mathematics) by Jean-Pierre Serre on page 84, page 100, and page 141
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