Mathematical Logic

This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions such as what is a mathematical proof, how can mathematical proofs be justified, and are there limitations to provability. It explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science, with complete proofs and numerous examples. The book also features modernizations, two additional important results, and is ideal for students beginning their studies in logic and the foundations of mathematics.

Format: Hardback
Publication date: 29 May 2021
Publisher: Springer International Publishing

This textbook delves into the realm of first-order logic, exploring its significance in the foundations of mathematics. It addresses fundamental questions such as what constitutes a mathematical proof, how they can be justified, and the boundaries of provability. By examining the capabilities and limitations of algorithms and proof methods in mathematics and computer science, the book aims to provide insights into the realm of mathematical proof.

The chapters in this textbook are meticulously structured, offering comprehensive proofs and numerous examples to aid in understanding. The book begins with motivating examples, laying the foundation for the subsequent chapters. These introductory chapters introduce the syntax and semantics of first-order logic, paving the way for advanced topics 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.

In this updated edition, numerous modernizations have been made, including two significant results: the decidability of Presburger arithmetic and the decidability of the weak monadic theory of the successor function. These results further enhance the textbook's relevance and importance in the field.

Mathematical Logic is an excellent resource for students embarking on their journey into logic and the foundations of mathematics. While primarily designed for graduate students or advanced undergraduates in mathematics or computer science, the book can also be valuable to individuals with a strong mathematical background and a basic understanding of abstract structures. The text assumes a level of mathematical maturity and familiarity with fundamental abstract concepts, such as those encountered in discrete mathematics or algebra.

Overall, this textbook offers a comprehensive and insightful exploration of first-order logic, its role in mathematics, and the techniques and methods employed in mathematical proof. It serves as a valuable resource for students, scholars, and professionals interested in the field.

Weight: 666g
Dimension: 161 x 243 x 21 (mm)
ISBN-13: 9783030738389