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Mathematical Logic and Model Theory

A Brief Introduction

  • Provides a streamlined yet easy-to-read introduction to a complete (first-order) formal system of mathematical logic

  • 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, this book develops a complete proof of Ax and Kochen's work on Artin's Conjecture about diophantine properties of p-adic number fields

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-X
  2. Alexander Prestel, Charles N. Delzell
    Pages 1-4
  3. Alexander Prestel, Charles N. Delzell
    Pages 5-60
  4. Alexander Prestel, Charles N. Delzell
    Pages 61-99
  5. Alexander Prestel, Charles N. Delzell
    Pages 101-127
  6. Alexander Prestel, Charles N. Delzell
    Pages 129-170
  7. Back Matter
    Pages 171-193

About this book

Introduction

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.

Keywords

Mathematical Logic Model Theory

Authors and affiliations

  1. 1.Fachbereich Mathematik und StatistikUniversität KonstanzKonstanzGermany
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA

Bibliographic information

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