"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."--Jacket. Read more...
Abstract:
This fresh edition of the straightforward introduction to modern mathematical logic retains its appeal to the intuition of working mathematicians, yet along with the material from the first edition, it has fresh chapters, one of which deals with Model Theory. Read more...
Author(s): Koblitz, Neal; Zilber, Boris; Manin Yu.I.
Series: Graduate texts in mathematics 53
Edition: 2
Publisher: Springer
Year: 2010
Language: English
Pages: 384
City: New York
Tags: Logic, Symbolic and mathematical.;Mathematische Logik.;Einführung.;Symbolisk logik.;Matematik.;Logic, Symbolic and mathematical
Content: 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. Gödel's incompleteness theorem
VIII. Recursive groups
IX. Constructive universe and computation --
Model theory: X. Model theory.
