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A Course in Mathematical Logic for Mathematicians Hardcover - 2009
by Manin, Yu. I./ Zilber, Boris
- New
- Hardcover
Description
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Details
- Title A Course in Mathematical Logic for Mathematicians
- Author Manin, Yu. I./ Zilber, Boris
- Binding Hardcover
- Edition 2nd ed
- Condition New
- Pages 384
- Volumes 1
- Language ENG
- Publisher Springer Verlag, U.S.A
- Date 2009
- Illustrated Yes
- Features Bibliography, Illustrated, Index
- Bookseller's Inventory # x-1441906142
- ISBN 9781441906144 / 1441906142
- Weight 1.63 lbs (0.74 kg)
- Dimensions 9.21 x 6.14 x 0.94 in (23.39 x 15.60 x 2.39 cm)
- Library of Congress subjects Logic, Symbolic and mathematical, Einf'uhrung
- Library of Congress Catalog Number 2009934521
- Dewey Decimal Code 511.3
From the publisher
From the rear cover
A Course in Mathematical Logic for Mathematicians, Second Edition offers a straightforward introduction to modern mathematical logic that will appeal to the intuition of working mathematicians. The book begins with an elementary introduction to formal languages and proceeds to a discussion of proof theory. It then presents several highlights of 20th century mathematical logic, including theorems of Gdel 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.
The exposition then moves to a discussion of computability theory that is based on the notion of recursive functions and stresses number-theoretic connections. The text present a complete proof of the theorem of Davis-Putnam-Robinson-Matiyasevich as well as a proof of Higman's theorem on recursive groups. Kolmogorov complexity is also treated.
Part III establishes the essential equivalence of proof theory and computation theory and gives applications such as Gdel's theorem on the length of proofs. A new Chapter IX, written by Yuri Manin, treats, among other things, a categorical approach to the theory of computation, quantum computation, and the P/NP problem. A new Chapter X, written by Boris Zilber, contains basic results of model theory and its applications to mainstream mathematics. This theory has 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, IL, USA, and Principal Researcher at the Steklov Institute of Mathematics, Moscow, Russia. Boris Zilber, Professor of Mathematical Logic at the University of Oxford, has contributed the Model Theory Chapter for the second edition.