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-稳定群和强级小集的几何学。 |
| Introduction 1 Structurese and Theories 1.1 Languages and Structures 1.2 Theories 1.3 Defiable Sets and Interpretability 1.4 Exercises and Remarks 2 Basic Techniqus 2.1 The Compactness Theoem 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 Elimintion 3.2 Algebraiclly 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 Hmogeneous 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 7 ω-Stable Groups 8 Geometry of Strongly Minimal Sets A Set Theory B Real Algebra References Index |
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