Mathematical Logic and Model Theory: A Brief Introduction

✍ Scribed by Alexander Prestel, Charles N. Delzell (auth.)

Publisher: Springer-Verlag London
Year: 2011
Tongue: English
Leaves: 205
Series: Universitext
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-X
Introduction....Pages 1-4
First-Order Logic....Pages 5-60
Model Constructions....Pages 61-99
Properties of Model Classes....Pages 101-127
Model Theory of Several Algebraic Theories....Pages 129-170
Back Matter....Pages 171-193

✦ Subjects

Mathematics, general; Mathematical Logic and Formal Languages

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