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

  • ISBN: 1461424798
  • Category: Math & Science
  • Author: Yu. I. Manin,Neal Koblitz,B. Zilber
  • Subcategory: Mathematics
  • Other formats: txt rtf doc azw
  • Language: English
  • Publisher: Springer; Softcover reprint of hardcover 2nd ed. 2010 edition (March 3, 2012)
  • Pages: 384 pages
  • FB2 size: 1937 kb
  • EPUB size: 1619 kb
  • Rating: 4.9
  • Votes: 506
Download A Course in Mathematical Logic for Mathematicians (Graduate Texts in Mathematics) fb2

Manin, Neal Koblitz, B. Zilber.

Manin, Neal Koblitz, B. 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.

Manin’s book on mathematical logic is addressed to a n with some knowledge of. .

Manin’s book on mathematical logic is addressed to a n with some knowledge of naive set theor.

Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The GTM series is easily identified by a white band at the top of the book.

Graduate Texts in Mathematics 5. In this book mathematical logic is presented both as a part of mathematics and as the result of its self-perception.

In this book mathematical logic is presented both as a part of mathematics and as the result of its self-perception. Thus, the substance of the book consists of dicult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought.

The text has been well received and is still used, although it has been out of print for some time.

A Course in Mathematical Logic for Mathematicians (Graduate Texts in Mathematics) - Y. Manin, N. Koblitz and B. He has also written series of books on differential geometry, so I guess he will probably continue with his project with at least one other book.

It then presents several highlights of 20th century mathematical logic, including theorems of Gödel and Tarski, and Cohen's theorem on the independence of the continuum hypothesis. A unique feature of the text is a discussion of quantum logic.

In this book mathematical logic is presented both as a part of mathe . 1. This book is above all addressed to mathematicians Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.

In this book mathematical logic is presented both as a part of mathe matics and as the result of its self-perception. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothe sis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.

1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.

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