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Author | : Raymond M. Smullyan |
Publisher | : Oxford University Press on Demand |
Total Pages | : 180 |
Release | : 1993 |
Genre | : Social Science |
ISBN | : 019508232X |
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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 |
Total Pages | : 184 |
Release | : 1993-01-28 |
Genre | : Mathematics |
ISBN | : 9780195344813 |
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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 |
Total Pages | : 416 |
Release | : 2013-03-14 |
Genre | : Philosophy |
ISBN | : 9401728666 |
Download Recursive Functions and Metamathematics Book in PDF, ePub and Kindle
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 | : Klaus Ambos-Spies |
Publisher | : |
Total Pages | : 408 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662178553 |
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Author | : Gerald E. Sacks |
Publisher | : Cambridge University Press |
Total Pages | : 361 |
Release | : 2017-03-02 |
Genre | : Mathematics |
ISBN | : 1107168430 |
Download Higher Recursion Theory Book in PDF, ePub and Kindle
This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Author | : Klaus Ambos-Spies |
Publisher | : Springer |
Total Pages | : 398 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540471421 |
Download Recursion Theory Week Book in PDF, ePub and Kindle
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 |
Total Pages | : 476 |
Release | : 2017-03-02 |
Genre | : Mathematics |
ISBN | : 1316739457 |
Download Metamathematics of First-Order Arithmetic Book in PDF, ePub and Kindle
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 |
Total Pages | : 395 |
Release | : 1999-09-30 |
Genre | : Philosophy |
ISBN | : 9780792359043 |
Download Recursive Functions and Metamathematics Book in PDF, ePub and Kindle
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 | : Ljubomir Lalov Ivanov |
Publisher | : |
Total Pages | : 268 |
Release | : 1986 |
Genre | : Recursion theory |
ISBN | : |
Download Algebraic Recursion Theory Book in PDF, ePub and Kindle
Author | : Hartley Rogers |
Publisher | : |
Total Pages | : 526 |
Release | : 1967 |
Genre | : Mathematics |
ISBN | : |
Download Theory of Recursive Functions and Effective Computability Book in PDF, ePub and Kindle