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Mathematical Logic and Model Theory

A Brief Introduction

  • Textbook
  • © 2011

Overview

Authors:
  1. Alexander Prestel

    1. Fachbereich Mathematik und Statistik, Universität Konstanz, Konstanz, Germany

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  2. Charles N. Delzell

    1. Department of Mathematics, Louisiana State University, Baton Rouge, USA

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    You can also search for this author in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Alexander Prestel, Charles N. Delzell
    Pages 1-4

  3. First-Order Logic

    • Alexander Prestel, Charles N. Delzell
    Pages 5-60

  4. Model Constructions

    • Alexander Prestel, Charles N. Delzell
    Pages 61-99

  5. Properties of Model Classes

    • Alexander Prestel, Charles N. Delzell
    Pages 101-127

  6. Model Theory of Several Algebraic Theories

    • Alexander Prestel, Charles N. Delzell
    Pages 129-170

  7. Back Matter

    Pages 171-193
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Keywords

About this book

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.

Authors and Affiliations

  • Fachbereich Mathematik und Statistik, Universität Konstanz, Konstanz, Germany

    Alexander Prestel

  • Department of Mathematics, Louisiana State University, Baton Rouge, USA

    Charles N. Delzell

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

  • Publisher: Springer London

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag London Limited 2011

  • Softcover ISBN: 978-1-4471-2175-6Published: 21 August 2011

  • eBook ISBN: 978-1-4471-2176-3Published: 21 August 2011

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: X, 194

  • Topics: Mathematics, general, Mathematical Logic and Formal Languages

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