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Manin, IU. I.
A course in mathematical logic for mathematicians / Yu. I. Manin ; chapters I-VIII translated from the Russian by Neal Koblitz ; with new chapters by Boris Zilber and Yuri I. Manin. - 2nd ed. - New York : Springer, 2010. - xvii, 384 p. : ill. ; 25 cm. - Graduate texts in mathematics ; 53 0072-5285 .
The first edition was published in 1977 with the title: A course in mathematical logic.
Includes bibliographical references (p. [379]-380) and index.
Provability: I. Introduction to formal languages ; II. Truth and deducibility ; III. The continuum problem and forcing ; IV. The continuum problem and constructible sets -- Computability: V. Recursive functions and Church's thesis ; VI. Diophantine sets and algorithmic undecidability -- Provability and computability: VII. G�odel's incompleteness theorem ; VIII. Recursive groups ; IX. Constructive universe and computation -- Model theory: X. Model theory.
"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 Godel 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 presents 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."--BOOK JACKET.
1441906142 (hbk.) 9781441906144 (hbk.) 9781441906151 1441906150
Logic, Symbolic and mathematical.
Einfuhrung.
Mathematische Logik.
QA9 / .M29613 2010
511.3 / M296
A course in mathematical logic for mathematicians / Yu. I. Manin ; chapters I-VIII translated from the Russian by Neal Koblitz ; with new chapters by Boris Zilber and Yuri I. Manin. - 2nd ed. - New York : Springer, 2010. - xvii, 384 p. : ill. ; 25 cm. - Graduate texts in mathematics ; 53 0072-5285 .
The first edition was published in 1977 with the title: A course in mathematical logic.
Includes bibliographical references (p. [379]-380) and index.
Provability: I. Introduction to formal languages ; II. Truth and deducibility ; III. The continuum problem and forcing ; IV. The continuum problem and constructible sets -- Computability: V. Recursive functions and Church's thesis ; VI. Diophantine sets and algorithmic undecidability -- Provability and computability: VII. G�odel's incompleteness theorem ; VIII. Recursive groups ; IX. Constructive universe and computation -- Model theory: X. Model theory.
"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 Godel 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 presents 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."--BOOK JACKET.
1441906142 (hbk.) 9781441906144 (hbk.) 9781441906151 1441906150
Logic, Symbolic and mathematical.
Einfuhrung.
Mathematische Logik.
QA9 / .M29613 2010
511.3 / M296