Mathematical Logic
Authors: Ebbinghaus, HeinzDieter, 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 firstorder logic plays in logical systems
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 About this Textbook

This textbook introduces firstorder 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 firstorder logic. After providing a sequent calculus for this logic, a Henkintype 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 firstorder 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

HeinzDieter 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)


Introduction
Pages 39

Syntax of FirstOrder Languages
Pages 1124

Semantics of FirstOrder Languages
Pages 2554

A Sequent Calculus
Pages 5570

The Completeness Theorem
Pages 7181

Table of contents (13 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Mathematical Logic
 Authors

 HeinzDieter Ebbinghaus
 Jörg Flum
 Wolfgang Thomas
 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
 9783030738396
 DOI
 10.1007/9783030738396
 Hardcover ISBN
 9783030738389
 Series ISSN
 00725285
 Edition Number
 3
 Number of Pages
 IX, 304
 Number of Illustrations
 17 b/w illustrations
 Topics