Mathematical Logic and Model Theory

A Brief Introduction
2011
ISBN: 978-1-4471-2175-6
Verlag: Springer

Buch, Englisch, 194 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 318 g

Reihe: Universitext

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Delzell, Charles N.

Prestel, Alexander

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten

Inhaltsverzeichnis

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