e-ISBN: 9781441906151 (e-isbn)
IR
E-4954
انگلیسی
IR
A course in mathematical logic for mathematicians
[Book]
/ Yu. I. Manin
; with new chapters by Boris Zilber and Yuri I. Manin
2nd ed.
New York
: Springer
, 2010.
xvii, 384 p. , ill.
(Graduate texts in mathematics,0072-5285
; 53.)
The first edition was published in 1977 with the title: A course in mathematical logic.
Print
Includes bibliographical references (p. [379]-380) and index.
Provability. Introduction 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. Geodel's incompleteness theorem -- Recursive groups-- Constructive universe and computation -- Model theory. 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.
Graduate texts in mathematics
53
Logic, Symbolic and mathematical
QA9
.
M29613
2010
Manin, eIiU. I.
Koblitz, Neal,1948-
Zilber, Boris
ایران
old catalog
p
BL
1
a
Y
