Model theory : an introduction = 模型论引论 / David Marker. — [Reprinted ed.]. — Beijing : Science Press ; New York : Springer, 2007. -- (51.33/M345(R))

Contents

    Contents
    
    Introduction
    1 Structures and Theories
    1.1 Languages and Structures
    1.2 Theories
    1.3 Definable Sets and Interpretability
    1.4 Exercises and Remarks
    2 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
    4 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
    5 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
    6 ω-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 ω-Stable Groups
    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