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001 978-1-4419-0615-1
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007 cr nn 008mamaa
008 100301s2010 xxu| s |||| 0|eng d
020 _a9781441906151
_9978-1-4419-0615-1
024 7 _a10.1007/978-1-4419-0615-1
_2doi
050 4 _aQA8.9-10.3
072 7 _aPBC
_2bicssc
072 7 _aPBCD
_2bicssc
072 7 _aMAT018000
_2bisacsh
082 0 4 _a511.3
_223
100 1 _aManin, Yu. I.
_eauthor.
245 1 2 _aA Course in Mathematical Logic for Mathematicians
_h[electronic resource] /
_cby Yu. I. Manin.
264 1 _aNew York, NY :
_bSpringer New York,
_c2010.
300 _bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v53
505 0 _aPROVABILITY -- to Formal Languages -- Truth and Deducibility -- The Continuum Problem and Forcing -- The Continuum Problem and Constructible Sets -- COMPUTABILITY -- Recursive Functions and Church’s Thesis -- Diophantine Sets and Algorithmic Undecidability -- PROVABILITY AND COMPUTABILITY -- Gödel’s Incompleteness Theorem -- Recursive Groups -- Constructive Universe and Computation -- MODEL THEORY -- Model Theory.
520 _aA 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 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. 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 Gödel'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.
650 0 _aMathematics.
650 0 _aLogic.
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aMathematics.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aLogic.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441906144
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v53
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-0615-1
912 _aZDB-2-SMA
999 _c110225
_d110225