A Course in Mathematical Logic
Seiten
1977
Springer-Verlag New York Inc.
978-0-387-90243-2 (ISBN)
Springer-Verlag New York Inc.
978-0-387-90243-2 (ISBN)
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Offers a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems.
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.
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.
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.
| Erscheint lt. Verlag | 1.8.1991 |
|---|---|
| Reihe/Serie | Graduate Texts in Mathematics ; 53 |
| Verlagsort | New York, NY |
| Sprache | englisch; russisch |
| Maße | 156 x 234 mm |
| Gewicht | 613 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre |
| ISBN-10 | 0-387-90243-0 / 0387902430 |
| ISBN-13 | 978-0-387-90243-2 / 9780387902432 |
| Zustand | Neuware |
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