The Resource A Course in Mathematical Logic for Mathematicians, by Yu. I. Manin, (electronic resource)

A Course in Mathematical Logic for Mathematicians, by Yu. I. Manin, (electronic resource)

Label
A Course in Mathematical Logic for Mathematicians
Title
A Course in Mathematical Logic for Mathematicians
Statement of responsibility
by Yu. I. Manin
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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 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
Member of
http://library.link/vocab/creatorName
Manin, Yu. I
Dewey number
511.3
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
SCaSFFCmQzs
Language note
English
LC call number
QA8.9-10.3
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Graduate Texts in Mathematics,
Series volume
53
http://library.link/vocab/subjectName
  • Logic, Symbolic and mathematical
  • Logic
  • Mathematical Logic and Foundations
  • Logic
Label
A Course in Mathematical Logic for Mathematicians, by Yu. I. Manin, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
PROVABILITY -- to Formal Languages -- Truth and Deducibility -- The Continuum Problem and Forcing -- The Continuum Problem and Constructible Sets -- COMPUTABILITY -- Recursive Functions and Church#x2019;s Thesis -- Diophantine Sets and Algorithmic Undecidability -- PROVABILITY AND COMPUTABILITY -- G#x00F6;del#x2019;s Incompleteness Theorem -- Recursive Groups -- Constructive Universe and Computation -- MODEL THEORY -- Model Theory
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (388 p.)
Form of item
online
Isbn
9786613569103
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4419-0615-1
Specific material designation
remote
System control number
  • (CKB)2510000000006513
  • (EBL)3064847
  • (SSID)ssj0000769153
  • (PQKBManifestationID)12352299
  • (PQKBTitleCode)TC0000769153
  • (PQKBWorkID)10767718
  • (PQKB)10813068
  • (DE-He213)978-1-4419-0615-1
  • (MiAaPQ)EBC3064847
  • (EXLCZ)992510000000006513
Label
A Course in Mathematical Logic for Mathematicians, by Yu. I. Manin, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
PROVABILITY -- to Formal Languages -- Truth and Deducibility -- The Continuum Problem and Forcing -- The Continuum Problem and Constructible Sets -- COMPUTABILITY -- Recursive Functions and Church#x2019;s Thesis -- Diophantine Sets and Algorithmic Undecidability -- PROVABILITY AND COMPUTABILITY -- G#x00F6;del#x2019;s Incompleteness Theorem -- Recursive Groups -- Constructive Universe and Computation -- MODEL THEORY -- Model Theory
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (388 p.)
Form of item
online
Isbn
9786613569103
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4419-0615-1
Specific material designation
remote
System control number
  • (CKB)2510000000006513
  • (EBL)3064847
  • (SSID)ssj0000769153
  • (PQKBManifestationID)12352299
  • (PQKBTitleCode)TC0000769153
  • (PQKBWorkID)10767718
  • (PQKB)10813068
  • (DE-He213)978-1-4419-0615-1
  • (MiAaPQ)EBC3064847
  • (EXLCZ)992510000000006513

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