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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...

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Bibliographic Details
Main Authors: Marcja, Annalisa, Toffalori, Carlo (Author)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 2003, 2003
Edition:1st ed. 2003
Series:Trends in Logic, Studia Logica Library
Subjects:
Mathematical Logic
Logic
Algebra
Mathematical Logic And Foundations
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

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