Overview
- Contains a new chapter on categorical approach to theory of computations, quantum computations, and P/NP problem
- New chapter containing basic results of Model Theory and its applications to mainstream mathematics
- Presents several highlights of mathematical logic of the 20th century including Gödel's and Tarski's Theorems, Cohen's Theorem on the independence of Continuum Hypothesis
- Complete proof of Davis-Putnam-Robinson-Matiyasevich theorem
- Discusses Kolmogorov complexity
- Includes supplementary material: sn.pub/extras
Part of the book series: Graduate Texts in Mathematics (GTM, volume 53)
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Keywords
Table of contents (10 chapters)
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COMPUTABILITY
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PROVABILITY AND COMPUTABILITY
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MODEL THEORY
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Reviews
From the reviews of the second edition:
"As one might expect from a graduate text on logic by a very distinguished algebraic geometer, this book assumes no previous acquaintance with logic, but proceeds at a high level of mathematical sophistication. Chapters I and II form a short course. Chapter I is a very informal introduction to formal languages, e.g., those of first order Peano arithmetic and of ZFC set theory. Chapter II contains Tarski's definition of truth, Gödel's completeness theorem, and the Löwenheim-Skolem theorem. The emphasis is on semantics rather than syntax. Some rarely-covered side topics are included (unique readability for languages with parentheses, Mostowski's transitive collapse lemma, formalities of introducing definable constants and function symbols). Some standard topics are neglected. (The compactness theorem is not mentioned!) The latter part of Chapter II contains Smullyan's quick proof of Tarski's theorem on the undefinability of truth in formal arithmetic, and an account of the Kochen-Specker "no hidden variables" theorem in quantum logic. There are digressions on philosophical issues (formal logic vs. ordinary language, computer proofs). A wealth of material is introduced in these first 100 pages of the book..."--MATHEMATICAL REVIEWS
“Manin’s book on mathematical logic is addressed to a working-mathematician with some knowledge of naive set theory … . incorporate some of the exciting developments in mathematical logic of the last four decades into this edition. … The exquisite taste and the elegant style of the author have produced an outstanding treatment of mathematical logic that allows one to understand some of the pillars of this area of mathematical research … and Manin’s original treatment of the subject provides an extraordinary introduction to mathematical logic.” (F. Luef, Internationale Mathematische Nachrichten, Issue 217, August, 2011)
“The new extended title of thisbook corresponds more to its concept, contents, spirit and style. The book is really addressed to mathematicians and introduces the reader to the glorious discoveries in logic during the last century through the difficult and subtle results, problems, proofs and comments. … due to the author’s brilliant style, each part of the book provokes new opinions and pleasure of a different understanding of basic results and ideas of contemporary mathematical logic.” (Branislav Boričić, Zentralblatt MATH, Vol. 1180, 2010)
Authors and Affiliations
Bibliographic Information
Book Title: A Course in Mathematical Logic for Mathematicians
Authors: Yu. I. Manin
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4419-0615-1
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature 2010
Hardcover ISBN: 978-1-4419-0614-4Published: 30 October 2009
Softcover ISBN: 978-1-4614-2479-6Published: 03 March 2012
eBook ISBN: 978-1-4419-0615-1Published: 13 October 2009
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 2
Number of Pages: XVIII, 384
Number of Illustrations: 12 b/w illustrations
Topics: Mathematical Logic and Foundations, Logic