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A course in mathematical logic for mathematicians

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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.
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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2010 English/International

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登録日 2020.06.27
更新日 2020.06.28