Logical Number Theory I

An Introduction

  • Craig Smoryński

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

  • Craig Smoryński
    • 1
  1. 1.WestmontUSA

Bibliographic information

  • 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
  • Print ISBN 978-3-540-52236-2
  • Online ISBN 978-3-642-75462-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book