Sorry, this item is not available in
Image not available for
Image not available

To view this video download Flash Player


Sign in to turn on 1-Click ordering
Sell Us Your Item
For a $10.92 Gift Card
Trade in
More Buying Choices
Have one to sell? Sell yours here
Tell the Publisher!
I'd like to read this book on Kindle

Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.

A Course in Mathematical Logic for Mathematicians (Graduate Texts in Mathematics) [Hardcover]

by Yu. I. Manin, NEAL Koblitz, B. Zilber

List Price: $69.95
Price: $54.28 & FREE Shipping. Details
You Save: $15.67 (22%)
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
Only 2 left in stock (more on the way).
Ships from and sold by Gift-wrap available.
Want it Monday, April 28? Choose One-Day Shipping at checkout. Details
Free Two-Day Shipping for College Students with Amazon Student


Amazon Price New from Used from
Hardcover $54.28  
Paperback --  
Sell Us Your Books
Get up to 80% back when you sell us your books, even if you didn't buy them at Amazon. Learn more

Book Description

October 30, 2009 1441906142 978-1441906144 2nd ed. 2010

The book starts with an elementary introduction to formal languages appealing to the intuition of working mathematicians and unencumbered by philosophical or normative prejudices such as those of constructivism or intuitionism. It proceeds to the Proof Theory and presents several highlights of Mathematical Logic of 20th century: Gödel's and Tarski's Theorems, Cohen's Theorem on the independence of Continuum Hypothesis. Unusual for books on logic is a section dedicated to quantum logic.

Then the exposition moves to the Computability Theory, based on the notion of recursive functions and stressing number{theoretic connections. A complete proof of Davis{Putnam{Robinson{Matiyasevich theorem is given, as well as a proof of Higman's theorem on recursive groups. Kolmogorov complexity is treated.

The third Part of the book establishes essential equivalence of proof theory and computation theory and gives applications such as Gödel's theorem on the length of proofs. The new Chapter IX, written for the second edition, treats, among other things, categorical approach to the theory of computation, quantum computation, and P/NP problem. The new Chapter X, written for the second edition by Boris Zilber, contains basic results of Model Theory and its applications to mainstream mathematics. This theory found deep applications in algebraic and Diophantine geometry.

Yuri Ivanovich Manin is Professor Emeritus at Max-Planck-Institute for Mathematics in Bonn, Germany, Board of Trustees Professor at the Northwestern University, Evanston, USA, and Principal Researcher at the Steklov Institute of Mathematics, Moscow, Russia. Boris Zilber, Professor of Mathematics at the University of Oxford, has been added to the second edition.

Frequently Bought Together

A Course in Mathematical Logic for Mathematicians (Graduate Texts in Mathematics) + Mathematical Logic (Addison-Wesley Series in Logic) + Mathematical Logic (Dover Books on Mathematics)
Price for all three: $114.62

Buy the selected items together

Customers Who Bought This Item Also Bought

Editorial 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 this book 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)

Language Notes

Text: English, Russian (translation) --This text refers to an alternate Hardcover edition.

Product Details

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

There are no customer reviews yet.
5 star
4 star
3 star
2 star
1 star
Share your thoughts with other customers

What Other Items Do Customers Buy After Viewing This Item?

Sell a Digital Version of This Book in the Kindle Store

If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store. Learn more


Topic From this Discussion
Can anyone help me with this book?
You are right, the idea is that there is no infinite descending chain in the von Neumann universe (because it is well-founded). The epsilons should appear inverted. It looks like there are several typos in the book:
Mar 17, 2011 by Marc Alcobé García |  See all 2 posts
Have something you'd like to share about this product?
Start a new discussion
First post:
Prompts for sign-in

Search Customer Discussions
Search all Amazon discussions

Look for Similar Items by Category