A Guide to Classical and Modern Model Theory
Since its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. It is a lively and fertile research area which deserves the attention of the mathematical world...
Main Authors: | , |
---|---|
Format: | eBook |
Language: | English |
Published: |
Dordrecht
Springer Netherlands
2003, 2003
|
Edition: | 1st ed. 2003 |
Series: | Trends in Logic, Studia Logica Library
|
Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 8.2 Algebraic varieties, ideals, types
- 8.3 Dimension and Morley rank
- 8.4 Morphisms and definable functions
- 8.5 Manifolds
- 8.6 Algebraic groups
- 8.7 The Mordell-Lang Conjecture
- 8.8 References
- O-minimality
- 9.1 Introduction
- 9.2 The Monotonicity Theorem
- 9.3 Cells
- 9.4 Cell decomposition and other theorems
- 9.5 Their proofs
- 9.6 Definable groups in o-minimal structures
- 9.7 O-minimality and Real Analysis
- 9.8 Variants on the o-minimal theme
- 9.9 No rose without thorns
- 9.10 References
- 4.5 The elimination of imaginaries sometimes fails
- 4.6 References
- Morley rank
- 5.1 A tale of two chapters
- 5.2 Definable sets
- 5.3 Types
- 5.4 Saturated models
- 5.5 A parenthesis: pure injective modules
- 5.6 Omitting types
- 5.7 The Morley rank, at last
- 5.8 Strongly minimal sets
- 5.9 Algebraic closure and definable closure
- 5.10 References
- ? -stability
- 6.1 Totally transcendental theories
- 6.2 ?-stable groups
- 6.3 ?-stable fields
- 6.4 Prime models
- 6.5 DCF0 revisited
- 6.6 Ryll-Nardzewski’s Theorem, and other things
- 6.7 References
- Classifying
- 7.1 Shelah’s Classification Theory
- 7.2 Simple theories
- 7.3 Stable theories
- 7.4 Superstable theories
- 7.5 ?-stable theories
- 7.6 Classifiable theories
- 7.7 Shelah’s Uniqueness Theorem
- 7.8 Morley’s Theorem
- 7.9 Biinterpretability and Zilber Conjecture
- 7.10 Two algebraicexamples
- 7.11 References
- Model Theory and Algebraic Geometry
- 8.1 Introduction
- Structures
- 1.1 Structures
- 1.2 Sentences
- 1.3 Embeddings
- 1.4 The Compactness Theorem
- 1.5 Elementary classes and theories
- 1.6 Complete theories
- 1.7 Definable sets
- 1.8 References
- Quantifier Elimination
- 2.1 Elimination sets
- 2.2 Discrete linear orders
- 2.3 Dense linear orders
- 2.4 Algebraically closed fields (and Tarski)
- 2.5 Tarski again: Real closed fields
- 2.6 pp-elimination of quantifiers and modules
- 2.7 Strongly minimal theories
- 2.8 o-minimal theories
- 2.9 Computational aspects of q. e
- 2.10 References
- Model Completeness
- 3.1 An introduction
- 3.2 Abraham Robinson’s test
- 3.3 Model completeness and Algebra
- 3.4 p-adic fields and Artin’s Conjecture
- 3.5 Existentially closed structures
- 3.6 DCF0
- 3.7 SCFp and DCFp
- 3.8 ACFA
- 3.9 References
- Elimination of imaginaries
- 4.1 Interpretability
- 4.2 Imaginary elements
- 4.3 Algebraically closed fields
- 4.4 Real closed fields