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Introduction to Model Theory
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Introduction to Model Theory

Introduction to Model Theory

Philipp Rothmaler

306 pages, parution le 13/03/2002

Résumé

Model theory investigates mathematical structures by means of formal languages. These so-called first-order languages have proved particularly useful. The text introduces the reader to the model theory of first-order logic, avoiding syntactical issues that are not too relevant to model-theory. In this spirit, the compactness theorem is proved via the algebraically useful ultraproduct technique, rather than via the completeness theorem of first-order logic. This leads fairly quickly to algebraic applications, like Malcev's local theorems (of group theory) and, after a little more preparation, also to Hilbert's Nullstellensatz (of field theory). Steinitz' dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal sets.

The final chapter is on the models of the first-order theory of the integers as an abelian group. This material appears here for the first time in a textbook of introductory level, and is used to give hints

Contents

Preface
Introduction
Interdependence chart
Notation

I: Basics

  • Structures
  • Languages
  • Semantics
II: Beginnings of Model Theory
  • The Finiteness Theorem
  • First Consequences of Finiteness Theorem
  • Malcev's Applications to Group Theory
  • Some Theory of Orderings
III: Basic Properties of Theories
  • Elementary Maps
  • Elimination
  • Chains
IV: Theories and Types
  • Types
  • Thick and Thin Models
  • Countable Complete Theories
V: Two Applications
  • Strong Minimal Theories
  • Z
Hints to Selected Exercises
Solutions for Selected Exercises
Bibliography and Hints for Further Reading
Symbols
Index

Caractéristiques techniques

  PAPIER
Éditeur(s) Gordon and Breach
Auteur(s) Philipp Rothmaler
Parution 13/03/2002
Nb. de pages 306
Format 15,5 x 23
Couverture Broché
Poids 470g
Intérieur Noir et Blanc
EAN13 9789056993139

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