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© 1991

Logical Number Theory I

An Introduction

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-x
  2. Craig Smoryński
    Pages 1-139
  3. Craig Smoryński
    Pages 140-265
  4. Craig Smoryński
    Pages 266-393
  5. Back Matter
    Pages 395-405

About this book

Introduction

Number theory as studied by the logician is the subject matter of the book. This first volume can stand on its own as a somewhat unorthodox introduction to mathematical logic for undergraduates, dealing with the usual introductory material: recursion theory, first-order logic, completeness, incompleteness, and undecidability. In addition, its second chapter contains the most complete logical discussion of Diophantine Decision Problems available anywhere, taking the reader right up to the frontiers of research (yet remaining accessible to the undergraduate). The first and third chapters also offer greater depth and breadth in logico-arithmetical matters than can be found in existing logic texts. Each chapter contains numerous exercises, historical and other comments aimed at developing the student's perspective on the subject, and a partially annotated bibliography.

Keywords

Diophantine equations Diophantische Gleichung Incompleteness Recursion Theory Rekursionstheorie Undecidability Unentscheidbarkeit Unvollständigkeit computability theory mathematical logic number theory proof

Authors and affiliations

  1. 1.WestmontUSA

Bibliographic information

  • Book Title Logical Number Theory I
  • Book Subtitle An Introduction
  • Authors Craig Smorynski
  • Series Title Universitext
  • DOI https://doi.org/10.1007/978-3-642-75462-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-52236-2
  • eBook ISBN 978-3-642-75462-3
  • Series ISSN 0172-5939
  • Series E-ISSN 2191-6675
  • Edition Number 1
  • Number of Pages X, 405
  • Number of Illustrations 2 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
    Mathematical Logic and Foundations
  • Buy this book on publisher's site
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