Extended! eBooks from the 'Springer Archives' only $/€/£ 8.99 each–save now!

Graduate Texts in Mathematics

Mathematical Logic

Authors: Ebbinghaus, Heinz-Dieter, Flum, Jörg, Thomas, Wolfgang

Free Preview
  • Explores additional important decidability results in this thoroughly updated new edition
  • Introduces mathematical logic by analyzing foundational questions on proofs and provability in mathematics
  • Highlights the capabilities and limitations of algorithms and proof methods both in mathematics and computer science
  • Examines advanced topics, such as linking logic with computability and automata theory, as well as the unique role first-order logic plays in logical systems
see more benefits

Buy this book

eBook 53,49 €
price for Spain (gross)
  • ISBN 978-3-030-73839-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 67,59 €
price for Spain (gross)
  • ISBN 978-3-030-73838-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science.

The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Gödel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindström's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function.

Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra.

About the authors

Heinz-Dieter Ebbinghaus is Professor Emeritus at the Mathematical Institute of the University of Freiburg. His work spans fields in logic, such as model theory and set theory, and includes historical aspects.

Jörg Flum is Professor Emeritus at the Mathematical Institute of the University of Freiburg. His research interests include mathematical logic, finite model theory, and parameterized complexity theory.

Wolfgang Thomas is Professor Emeritus at the Computer Science Department of RWTH Aachen University. His research interests focus on logic in computer science, in particular logical aspects of automata theory.

Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook 53,49 €
price for Spain (gross)
  • ISBN 978-3-030-73839-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 67,59 €
price for Spain (gross)
  • ISBN 978-3-030-73838-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Mathematical Logic
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
291
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-73839-6
DOI
10.1007/978-3-030-73839-6
Hardcover ISBN
978-3-030-73838-9
Series ISSN
0072-5285
Edition Number
3
Number of Pages
IX, 304
Number of Illustrations
17 b/w illustrations
Topics