Model Theory, Algebra, and Geometry by Deirdre Haskell, Anand Pillay and Charles Steinhorn
About this book :-
Model theory is a branch of mathematical logic that has found applications in several areas of algebra and geometry. This text explores how model theory applies to various areas of algebra and geometry. The book demonstrates how abstract concepts in model theory can lead to significant results in geometry, such as the proof of the Mordell–Lang conjecture for function fields in positive characteristic. The content is structured to provide both foundational knowledge and insights into advanced 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.
The book begins with an introduction to model theory by David Marker. It then broadens into three components: pure model theory (Bradd Hart, Dugald Macpherson), geometry (Barry Mazur, Ed Bierstone and Pierre Milman, Jan Denef), and the model theory of fields (Marker, Lou van den Dries, Zoé Chatzidakis).
This book is suitable for students seeking to understand algebra through practical applications and is a valuable resource for those preparing for precalculus courses.
Book Detail :-
Title:
Model Theory, Algebra, and Geometry by Deirdre Haskell, Anand Pillay and Charles Steinhorn
Publisher:
Cambridge University Press
Year:
2010
Pages:
236
Type:
PDF
Language:
English
ISBN-10 #:
0521143497
ISBN-13 #:
978-0521143493
License:
Linked Content Owned by Author
Amazon:
Amazon
About Author :-
The author
Deirdre Haskell
is a professor at McMaster University specializing in model-theoretic algebra, focusing on applying model theory techniques to algebraic structures like valued fields. Anand Pillay is a British mathematician and logician known for his work in model theory and its applications in algebra and number theory. Charles Steinhorn is a professor at Vassar College whose research interests lie in model theory, particularly in the areas of stability theory and its applications to algebra and geometry.
Book Contents :-
1. Introduction to Model Theory by David Marker
2. Classical Model Theory of Fields by Lou Van Den Dries
3. Model Theory of Differential Fields by David Marker
4. A Survey on the Model Theory of Difference Fields by Zoe Chatzidakis
5. Notes on o-Minimality and Variations by Dugald Macpherson
6. Stability Theory and its Variations by Bradd Hart
7. Subanalytic Geometry by Edward Bierstone and Pierre D Milman
8. Arithmeic and Geometric Applications of Quantifier Elimination for Valued Fields by Jan Denef
9. Abelian Varieties and the Mordell Lang Conjecture by Barry Mazur
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