An Introduction To Stability Theory

Book Details:

• Publisher: Dover

• Author: Pillay, Anand

• Language: English

• Edition: N/A

• ISBN: 9780486468969

• Pages: 160

• Cover: Paperback

• Dimensions: 9.1 x 6.1 x 0.4 inches

About The Book:

"Stability Theory" by Anand Pillay offers a rigorous yet accessible introduction to the fundamental concepts of stability theory in mathematics. Designed for graduate students, professional mathematicians, and computer scientists, the book provides a solid foundation in the key ideas and techniques of the subject. The text is full of examples, theorems, propositions, and problems, which make it both a comprehensive study tool and a reference guide.

The first chapter introduces the foundational concepts of definable type, heir, and coheir, followed by a discussion of stability and order. Pillay goes on to define forking, following the approach of Lascar and Poizat, and explores the relationship between forking and the definability of types. Subsequent chapters delve into more advanced topics such as superstability, dividing and ranks, and the connection between types and sets of indiscernibles.

The book concludes with significant results, including proofs of the Morley and Baldwin-Lachlan theorems, and introduces an extension of dimension theory that incorporates orthogonality of types in addition to regular types. With its clear explanations and structured presentation, this book is an essential resource for anyone studying or working in the field of logic and mathematics.