模型论引论

　　本书以现代观点介绍模型论，着重强调其在代数学中的应用。前半部分包括模型构造技巧的经典论述，如类型空间，素模型，饱和模型，可数模型，不可辨元等理论及其应用。在书中后半部分，作者首先介绍莫利的范畴性定理，随之讨论稳定性理论，着重论述Ω-稳定性理论。最后，作者举例阐明了赫鲁索夫斯基如何将这些理论运用于丢番图几何。本书显著特色之一是包含一些其他入门型教材所未涉及的重要论题，如Ω-稳定群和强极小集的几何学。.作者David Marker是伊利诺斯大学芝加哥分校的数学教授，主要研究数学逻辑和模型论及其在代数和几何中的应用。本书基于作者1998年在数学科学研究所发表的系列演讲。...

暂缺《模型论引论》作者简介

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