# 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)

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

### 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

• Book Title Mathematical Logic and Model Theory
• Book Subtitle A Brief Introduction
• Authors Alexander Prestel
Charles N. Delzell
• Series Title Universitext
• DOI https://doi.org/10.1007/978-1-4471-2176-3
• Copyright Information Springer-Verlag London Limited 2011
• Publisher Name Springer, London
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Softcover ISBN 978-1-4471-2175-6
• eBook ISBN 978-1-4471-2176-3
• Series ISSN 0172-5939
• Series E-ISSN 2191-6675
• Edition Number 1
• Number of Pages X, 194
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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