Mathematical Logic and Model Theory

A Brief Introduction
 
 
Springer (Verlag)
  • erschienen am 21. August 2011
 
  • Buch
  • |
  • Softcover
  • |
  • 204 Seiten
978-1-4471-2175-6 (ISBN)
 
Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.
Paperback
2011
  • Englisch
  • London
  • |
  • Großbritannien
  • Für Beruf und Forschung
  • |
  • Upper undergraduate
  • Broschur/Paperback
biography
  • Höhe: 235 mm
  • |
  • Breite: 155 mm
  • |
  • Dicke: 11 mm
  • 318 gr
978-1-4471-2175-6 (9781447121756)
10.1007/978-1-4471-2176-3
weitere Ausgaben werden ermittelt

First-Order Logic.- Model Constructions.- Properties of Model Classes.- Model Theory of Several Algebraic Theories

Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra.

As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields.

The character of model theoretic constructions and results differs significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4).

This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.
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