A course in mathematical logic for mathematicians
|概要||"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 b...ook 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.続きを見る|
|目次||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.
|本文を見る||Full text available from Springer Mathematics and Statistics eBooks 2010 English/International|