Universitext

Mathematical Logic and Model Theory

A Brief Introduction

Authors: Prestel, Alexander, Delzell, Charles

  • 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
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eBook $44.99
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  • ISBN 978-1-4471-2176-3
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  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-1-4471-2175-6
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  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this Textbook

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 (5 chapters)

  • Introduction

    Prestel, Alexander (et al.)

    Pages 1-4

  • First-Order Logic

    Prestel, Alexander (et al.)

    Pages 5-60

  • Model Constructions

    Prestel, Alexander (et al.)

    Pages 61-99

  • Properties of Model Classes

    Prestel, Alexander (et al.)

    Pages 101-127

  • Model Theory of Several Algebraic Theories

    Prestel, Alexander (et al.)

    Pages 129-170

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-4471-2176-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-1-4471-2175-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Logic and Model Theory
Book Subtitle
A Brief Introduction
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-1-4471-2176-3
DOI
10.1007/978-1-4471-2176-3
Softcover ISBN
978-1-4471-2175-6
Series ISSN
0172-5939
Edition Number
1
Number of Pages
X, 194
Topics