Saturated Model Theory (2nd Edition)

By: Gerald E Sacks

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Hardcover | 2 October 2009 | Edition Number 2

At a Glance

Hardcover
220 Pages

Edition Type
Revised

Dimensions(cm)
23.4 x 16.0 x 2.0

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This book contains the material for a first course in pure model theory with applications to differentially closed fields. Topics covered in this book include saturated model criteria for model completeness and elimination of quantifiers; Morley rank and degree of element types; categoricity in power; two-cardinal theorems; existence and uniqueness of prime model extensions of substructures of models of totally transcendental theories; and homogeneity of models of 1-categorical theories.

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Introduction	p. 1
Ordinals and Diagrams	p. 5
Similarity Types of Structures	p. 7
Monomorphisms and Substructures	p. 9
First Order Languages	p. 11
Elementary Equivalence	p. 14
Elementary Monomorphisms	p. 16
The Fundamental Existence Theorem	p. 18
Model Completeness	p. 24
Model Completeness of Algebraically Closed Fields	p. 28
Direct Systems of Structures	p. 32
Skolemization of Structures	p. 37
Model Completions	p. 39
Substructure Completeness	p. 43
Countability Proviso with Exceptions	p. 47
Element Types	p. 48
Saturated Structures	p. 51
Elimination of Quantifiers for Real Closed Fields	p. 58
Omitting a Type	p. 64
?-Stable Theories	p. 69
Homogeneous Structures	p. 72
The Number of Countable Models	p. 77
Vaught's Two-Cardinal Theorem	p. 82
Chang's Two-Cardinal Theorem	p. 87
Keisler's Two-Cardinal Theorem	p. 93
Categories and Functors	p. 101
Inverse Systems of Compact Hausdorff Spaces	p. 104
Towards Morley's Analysis of l-Types	p. 106
The Cantor-Bendixson Derivative	p. 109
The Morley Derivative	p. 112
Autonomous Subcategories	p. 117
Bounds on the Ranks of 1-Types	p. 121
Prime Model Extensions	p. 127
Prime Extensions of Wellordered Chains	p. 135
Order Indiscernibles	p. 138
Indiscernibles and ?-Stability	p. 143
Shelah's Uniqueness Theorem	p. 153
Categoricity in Some Uncountable Power	p. 160
Minimal Generators and ?₁-Categoricity	p. 164
The Baldwin-Lachlan Theorem	p. 172
Differential Fields of Characteristic 0	p. 185
The Differential Closure	p. 191
Some Other Reading	p. 195
References	p. 199
Notation Index	p. 201
Index	p. 205
Table of Contents provided by Ingram. All Rights Reserved.

Saturated Model Theory (2nd Edition)

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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