模型论引论

Introduction

StructuresandTheories

1.1LanguagesandStructures

1.2Theories

1.3DefinableSetsandInterpretability

1.4ExercisesandRemarks

BasicTechniques

2.1TheCompactnessTheorem

2.2CompleteTheories

2.3UpandDown

2.4BackandForth

2.5ExercisesandRemarks

3AlgebraicExamples

3.1QuantifierElimination

3.2AlgebraicallyClosedFields

3.3RealClosedFields

3.4ExercisesandRemarks

RealizingandOmittingTypes

4.1Types

4.2OmittingTypesandPrimeModels

4.3SaturatedandHomogeneousModels

4.4TheNumberofCountableModels

4.5ExercisesandRemarks

Indiscernibles

5.1PartitionTheorems

5.2OrderIndiscernibles

5.3AMany-ModelsTheorem

5.4AnIndependenceResultinArithmetic

5.5ExercisesandRemarks

w-StableTheories

6.1UncountablyCategoricalTheories

6.2MorleyRank

6.3ForkingandIndependence

6.4UniquenessofPrimeModelExtensions

6.5MorleySequences

6.6ExercisesandRemarks

w-StableGroups

7.1TheDescendingChainCondition

7.2GenericTypes

7.3TheIndecomposabilityTheorem

7.4DefinableGroupsinAlgebraicallyClosedFields

7.5FindingaGroup

7.6ExercisesandRemarks

8GeometryofStronglyMinimalSets

8.1Pregeometries

8.2CanonicalBasesandFamiliesofPlaneCurves

8.3GeometryandAlgebra

8.4ExercisesandRemarks

ASetTheory

BRealAlgebraReferences

Index

　　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。