模型論引論

Introduction
Structures and Theories
1.1 Languages and Structures
1.2 Theories
1.3 Definable Sets and Interpretability
1.4 Exercises and Remarks
Basic Techniques
2.1 The Compactness Theorem
2.2 Complete Theories
2.3 Up and Down
2.4 Back and Forth
2.5 Exercises and Remarks
3 Algebraic Examples
3.1 Quantifier Elimination
3.2 Algebraically Closed Fields
3.3 Real Closed Fields
3.4 Exercises and Remarks
Realizing and Omitting Types
4.1 Types
4.2 Omitting Types and Prime Models
4.3 Saturated and Homogeneous Models
4.4 The Number of Countable Models
4.5 Exercises and Remarks
Indiscernibles
5.1 Partition Theorems
5.2 Order Indiscernibles
5.3 A Many-Models Theorem
5.4 An Independence Result in Arithmetic
5.5 Exercises and Remarks
w-Stable Theories
6.1 Uncountably Categorical Theories
6.2 Morley Rank
6.3 Forking and Independence
6.4 Uniqueness of Prime Model Extensions
6.5 Morley Sequences
6.6 Exercises and Remarks
……
7.1 The Descending Chain Condition
7.2 Generic Types
7.3 The Indecomposability Theorem
7.4 Definable Groups in Algebraically Closed Fields
7.5 Finding a Group
7.6 Exercises and Remarks
8 Geometry of Strongly Minimal Sets
8.1 Pregeometries
8.2 Canonical Bases and Families of Plane Curves
8.3 Geometry and Algebra
8.4 Exercises and Remarks
A Set Theory
B Real Algebra
References
Index