Universitext

A Concise Introduction to Mathematical Logic

Authors: Rautenberg, Wolfgang

  • Contains chapter summaries
  • Includes section summaries
  • Offers detailed illustrations
  • Provides exercises at the ends of chapters or sections
  • Contains solutions to selected exercises in the book
  • Includes a separate solutions manual on the Internet
see more benefits

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4419-1221-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-1-4419-1220-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Traditional logic as a part of philosophy is one of the oldest scientific disciplines and can be traced back to the Stoics and to Aristotle. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, and others to create a logistic foundation for mathematics. It steadily developed during the twentieth century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy.

This book treats the most important material in a concise and streamlined fashion. The third edition is a thorough and expanded revision of the former. Although the book is intended for use as a graduate text, the first three chapters can easily be read by undergraduates interested in mathematical logic. These initial chapters cover the material for an introductory course on mathematical logic, combined with applications of formalization techniques to set theory. Chapter 3 is partly of descriptive nature, providing a view towards algorithmic decision problems, automated theorem proving, non-standard models including non-standard analysis, and related topics.

The remaining chapters contain basic material on logic programming for logicians and computer scientists, model theory, recursion theory, Gödel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. Each section of the seven chapters ends with exercises some of which of importance for the text itself. There are hints to most of the exercises in a separate file Solution Hints to the Exercises which is not part of the book but is available from the author’s website.

Reviews

From the reviews of the third edition:

“Wolfgang Rautenberg’s A Concise Introduction to Mathematical Logic is a pretty ambitious undertaking, seeing that at the indicated introductory level it covers ‘classical material … and Godel’s incompleteness theorems, as well as some topics motivated by applications, such as chapter on logic programming’ (from the Foreword by Lev Beklemishev). … The third edition … is a fine piece of scholarship and will more than repay the efforts of the committed student who chooses this means as an entry into modern mathematical logic.” (Michael Berg, The Mathematical Association of America, June, 2010)

“This is essentially the English translation of the third edition of the German version [Einführung in die mathematische Logik. Ein Lehrbuch. Wiesbaden: Vieweg+Teubner (2008; Zb1 1152.03-002)] of this well-written textbook … . The book remains one of the most recommendable introductions into mathematical logic for mathematicians, and well-suited for computer scientists too.” (Siegfried J. Gottwald, Zentralblatt MATH, Vol. 1185, 2010)


Table of contents (7 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4419-1221-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-1-4419-1220-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
A Concise Introduction to Mathematical Logic
Authors
Series Title
Universitext
Copyright
2010
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4419-1221-3
DOI
10.1007/978-1-4419-1221-3
Softcover ISBN
978-1-4419-1220-6
Series ISSN
0172-5939
Edition Number
3
Number of Pages
XXII, 320
Number of Illustrations and Tables
25 b/w illustrations
Topics