Sacks G.E. Saturated model theory

2nd Ed. — World Scientific, 2010. — xii, 207 p. — ISBN13: 978-981-283-381-5, ISBN10: 981-283-381-1.
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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.Ordinals and Diagrams
Similarity Types of Structures
Monomorphisms and Substructures
First Order Languages
Elementary Equivalence
Elementary Monomorphisms
The Fundamental Existence Theorem
Model Completeness
Model Completeness of Algebraically Closed Fields
Direct Systems of Structures
Skolemization of Structures
Model Completions
Substructure Completeness
Countability Proviso with Exceptions
Element Types
Saturated Structures
Elimination of Quantifiers for Real Closed Fields
Omitting a Type
ω-Stable Theories
Homogeneous Structures
The Number of Countable Models
Vaught’s Two-Cardinal Theorem
Chang’s Two-Cardinal Theorem
Keisler’s Two-Cardinal Theorem
Categories and Functors
Inverse Systems of Compact Hausdorff Spaces
Towards Morley’s Analysis of l-Types
The Cantor–Bendixson Derivative
The Morley Derivative
Autonomous Subcategories
Bounds on the Ranks of 1-Types
Prime Model Extensions
Prime Extensions of Wellordered Chains
Order Indiscernibles
Indiscernibles and ω-Stability
Shelah’s Uniqueness Theorem
Categoricity in Some Uncountable Power
Minimal Generators and ω₁-Categoricity
The Baldwin–Lachlan Theorem
Differential Fields of Characteristic 0
The Differential Closure
Some Other ReadingNotation Index