A course in mathematical logic
著者
書誌事項
A course in mathematical logic
（Graduate texts in mathematics, 53）
Springer, c1977
- : us
- : gw
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注記
Includes index
内容説明・目次
- 巻冊次
-
: us ISBN 9780387902432
内容説明
This book is a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last 10 to 15 years, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems. The book contains the first textbook presentation of Matijasevic's result. The central notions are provability and computability; the emphasis of the presentation is on aspects of the theory which are of interest to the working mathematician. Many of the approaches and topics covered are not standard parts of logic courses; they include a discussion of the logic of quantum mechanics, Goedel's constructible sets as a sub-class of von Neumann's universe, the Kolmogorov theory of complexity. Feferman's theorem on Goedel formulas as axioms and Highman's theorem on groups defined by enumerable sets of generators and relations. A number of informal digressions concerned with psychology, linguistics, and common sense logic should interest students of the philosophy of science or the humanities.
目次
Contents: 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: Godel's Incompleteness Theorem. Recursive Groups.- Index.
- 巻冊次
-
: gw ISBN 9783540902430
内容説明
This text on mathematical logic presents the reader with several of the most significant discoveries of the last 10 to 15 years, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems. The book contains the first textbook presentation of Matijasevic's result. The central notions are provability and computability; the emphasis of the presentation is on aspects of the theory which are of interest to the working mathematician. Many of the approaches and topics covered are not standard parts of logic courses. They include a discussion of the logic of quantum mechanics, Goedel's constructible sets as a sub-class of von Neumann's universe, the Kolmogorov theory of complexity, Feferman's theorem on Goedel formulae as axioms and Highman's theorem on groups defined by enumerable sets of generators and relations.
目次
- 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
- Goedel's incompleteness theorem
- recursive groups.
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