Geometric Stability Theory

by Anand Pillay

Overview

This book gives an account of the fundamental results in geometric stability theory, a subject that has grown out of categoricity and classification theory. This approach studies the fine structure of models of stable theories, using the geometry of forking; this often achieves global results relevant to classification theory. Topics range from Zilber-Cherlin classification of infinite locally finite homogenous geometries, to regular types, their geometries, and their role in superstable theories. The structure and existence of definable groups is featured prominently, as is work by Hrushovski. The book is unique in the range and depth of material covered and will be invaluable to anyone interested in modern model theory.

Product Details

ISBN-13:	9780198534372
Publisher:	Oxford University Press, USA
Publication date:	09/28/1996
Series:	Oxford Logic Guides Series , #32
Edition description:	New Edition
Pages:	376
Product dimensions:	6.31(w) x 9.50(h) x 0.99(d)

Table of Contents

1. Stability Theory
2. The Classical Finte Rank Theory
3. Quasi Finite Axiomatizability
4. 1-Based Theories and Groups
5. Groups and Geometries
6. Unidimensional Theories
7. Regular Types
8. Superstable Theories

Editorial Reviews

"A nice introduction to the latest achievements of geometric model theory (Lie coordinatizable structures and simple theories). . . .The book should be on the bookshelf of anyone with an interest in stability theory. It is written in an elegant and enjoyable manner and can be recommended even to undergraduates who have already learnt the basic facts of model theory." —Mathematical Reviews

"The subject of the book is at the very heart of modern model theory, and is close in spirit to what should be called foundations of mathematics. Geometric stability theory as presented in this book, concentrates on the basic structural properties of stable structures. The principal tools for characterizing stable structures are various dimensions (ranks) and special geometric configurations. The choice of the material for this book is, in my opinion, exactly optimal. The language and the proofs are very clear. I would recommend the book for postgraduate students specializing in model theory and for all those who would like to deepen their expertise in modern model theory and its application." -Boris Zil'ber, The Journal of Sumbolic Logic, Vol 63, No. 3, Sept 1998

From the Publisher