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Classification Theory and the Number of Non-Isomorphic Models

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In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text.

The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m|M|. This theorem is also the subject of Chapter XIII

Author(s): Saharon Shelah
Series: Studies in Logic and the Foundations of Mathematics 92
Edition: 2nd
Publisher: North Holland
Year: 1990

Commentary: missing pages v-viii (table of contents), no cover
Pages: 733

Content:
Edited by
Pages ii-iii

Copyright page
Page iv

Acknowledgements
Page ix

Introduction
Pages xi-xiv

Introduction to the Revised Edition
Pages xv-xvi

Open Problems
Pages xvii-xxii

Added in Proof
Pages xxiii-xxx

Notation
Pages xxxi-xxxiv

Chapter I Preliminaries
Pages 1-17

Chapter II Ranks and Incomplete Types
Pages 18-81

Chapter III Global Theory
Pages 82-149

Chapter IV Prime Models
Pages 150-222

Chapter V More on Types and Saturated Models
Pages 223-320

Chapter VI Saturation of Ultraproducts
Pages 321-396

Chapter VII Construction of Models
Pages 397-439

Chapter VIII The Number of Non-Isomorphic Models in Pseudo-Elementary Classes
Pages 440-478

Chapter IX Categoricity and the Number of Models in Elementary Classes
Pages 479-507

Chapter X Classification for FaN0-Saturated Models
Pages 508-556

Chapter XI The Decomposition Theorem
Pages 557-589

Chapter XII The Main Gap for Countable Theories
Pages 590-621

Chapter XIII for Thomas the Doubter
Pages 622-652

Appendix
Pages 653-672

Historical Remarks
Pages 673-683

References
Pages 684-690

Index of Definitions and Abbreviations
Pages 691-702

Index of Spmbols
Pages 703-705