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Author: Raymond M. Smullyan
Publisher: Oxford University Press on Demand
ISBN: 019508232X
Category : Social Science
Languages : en
Pages : 180
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Book Description
This work is a sequel to the author's G�del's Incompleteness Theorems, though it can be read independently by anyone familiar with G�del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
Author: Raymond M. Smullyan
Publisher: Oxford University Press on Demand
ISBN: 019508232X
Category : Social Science
Languages : en
Pages : 180
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Book Description
This work is a sequel to the author's G�del's Incompleteness Theorems, though it can be read independently by anyone familiar with G�del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
Author: Raymond M. Smullyan
Publisher: Oxford University Press
ISBN: 9780195344813
Category : Mathematics
Languages : en
Pages : 184
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Book Description
This work is a sequel to the author's Gödel's Incompleteness Theorems, though it can be read independently by anyone familiar with Gödel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
Author: Roman Murawski
Publisher: Springer Science & Business Media
ISBN: 9401728666
Category : Philosophy
Languages : en
Pages : 416
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Book Description
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
Author: Gerald E. Sacks
Publisher: Cambridge University Press
ISBN: 1107168430
Category : Mathematics
Languages : en
Pages : 361
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Book Description
This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Author: Klaus Ambos-Spies
Publisher:
ISBN: 9783662178553
Category :
Languages : en
Pages : 408
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Book Description
Author: Klaus Ambos-Spies
Publisher: Springer
ISBN: 3540471421
Category : Mathematics
Languages : en
Pages : 398
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Book Description
These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field. Other topics covered include computational complexity theory, generalized recursion theory, proof theoretic questions in recursion theory, and recursive mathematics.
Author: Petr Hájek
Publisher: Cambridge University Press
ISBN: 1316739457
Category : Mathematics
Languages : en
Pages : 476
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Book Description
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).
Author: Roman Murawski
Publisher: Springer
ISBN: 9780792359043
Category : Philosophy
Languages : en
Pages : 395
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Book Description
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
Author: Hartley Rogers
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 526
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Book Description
Author: Ljubomir Lalov Ivanov
Publisher:
ISBN:
Category : Recursion theory
Languages : en
Pages : 268
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Book Description
