Mathematical Logic (3/e)

丛 书 名：Graduate Texts in Mathematics

版本说明：3

作     者：Heinz-Dieter Ebbinghaus Jörg Flum Wolfgang Thomas 

I S B N：(纸本) 9783030738389 

出 版 社：Springer 

出 版 年：2021年

摘      要：Explores additional important decidability results in this thoroughly updated new editionIntroduces mathematical logic by analyzing foundational questions on proofs and provability in mathematicsHighlights the capabilities and limitations of algorithms and proof methods both in mathematics and computer scienceExamines advanced topics, such as linking logic with computability and automata theory, as well as the unique role first-order logic plays in logical systemsThis 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 *** 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 *** 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 prer