ISBN: 9783030738389 - mathematical logic (graduate texts in mathematics, 291, band 291) (8 Ergebnisse)

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Hardback. Zustand: Good. What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe- matical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godel's completeness theorem, which shows that the con- sequence relation coincides with formal provability: By means of a calcu- lus consisting of simple formal inference rules, one can obtain all conse- quences of a given axiom system (and in particular, imitate all mathemat- ical proofs). A short digression into model theory will help us to analyze the expres- sive power of the first-order language, and it will turn out that there are certain deficiencies. For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.…

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Zustand: New. 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 o.

Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.…

Hardcover. Zustand: Brand New. 3rd edition. 304 pages. 9.50x6.25x1.00 inches. In Stock.