Simplicity Theory
1st Edition
Published on 5. October 2013
235 pages
978-0-19-151158-5 (ISBN)
Description
An up-to-date account of the current techniques and results in Simplicity Theory, which has been a focus of research in model theory for the last decade. Suitable for logicians, mathematicians and graduate students working on model theory.
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Content
- Cover
- Contents
- 1 Introduction
- 1.1 Model Theory
- 1.2 Stability
- 1.3 Bibliographical Remarks
- 2 Dividing, Forking, and Simplicity
- 2.1 Dividing and Forking
- 2.2 Simplicity and Forking
- 2.3 D[sub(f,k)]-Ranks and the Tree Property
- 2.4 Fundamental Theorem of Forking
- 2.5 Ranks and Supersimple Theories
- 2.6 Examples of Simple Theories
- 2.7 Bibliographical Remarks
- 3 Lascar Strong Types and Type Amalgamation
- 3.1 Lascar Strong Types
- 3.2 Type Amalgamation
- 3.3 Characterizing Simple Theories
- 3.4 Bibliographical Remarks
- 4 Hyperimaginaries and Canonical Bases
- 4.1 Hyperimaginaries
- 4.2 Non-forking Independence of Hyperimaginaries
- 4.3 Canonical Bases
- 4.4 Forking Relationships between Types
- 4.5 Bibliographical Remarks
- 5 Elimination of Hyperimaginaries
- 5.1 The Lascar Group
- 5.2 Lascar Types Are Strong Types in Low Theories
- 5.3 Elimination of Finitary Hyperimaginaries for Small Theories
- 5.4 Elimination of Hyperimaginaries for Supersimple Theories
- 5.5 Definability
- 5.6 Bibliographical Remarks
- 6 Constructing Simple Structures
- 6.1 Modularity and CM-Triviality
- 6.2 Hrushovski Construction
- 6.3 Generic Predicates/Automorphisms and Lovely Pairs
- 6.4 Bibliographical Remarks
- 7 Groups
- 7.1 Type-Definable Groups
- 7.2 Hyperdefinable Groups
- 7.3 Commensurativity and Local Connectedness
- 7.4 1-Based Groups
- 7.5 Supersimple Groups
- 7.6 Generically Given Partial Groups and Homogeneous Spaces
- 7.7 Bibliographical Remarks
- 8 A Geometry of Forking
- 8.1 SU-Rank 1 Types
- 8.2 Non-affine Locally Modular Types
- 8.3 1-Based Types
- 8.4 Bibliographical Remarks
- 9 Generalized Amalgamation and the Group Configuration Theorem
- 9.1 Generalized Amalgamation
- 9.2 The Group Configuration
- 9.3 The Generic Group Operation on G/R
- 9.4 An Application to 1-Based Theories
- 9.5 Recovering the Hyperdefinable Group Action
- 9.6 Bibliographical Remarks
- References
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- L
- M
- O
- P
- R
- S
- T
- W
- Z
