Recursion Theory For Metamathematics
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Author | : Raymond M. Smullyan |
Publisher | : Oxford University Press, USA |
Total Pages | : 180 |
Release | : 1993 |
Genre | : Computers |
ISBN | : 019508232X |
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 | : Raymond M. Smullyan |
Publisher | : Oxford University Press |
Total Pages | : 180 |
Release | : 1993-01-28 |
Genre | : Mathematics |
ISBN | : 0195344812 |
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 |
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 |
Author | : Klaus Ambos-Spies |
Publisher | : Springer |
Total Pages | : 398 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540471421 |
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 | : Roman Murawski |
Publisher | : Springer |
Total Pages | : 395 |
Release | : 1999-09-30 |
Genre | : Philosophy |
ISBN | : 9780792359043 |
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 |
Total Pages | : 361 |
Release | : 2017-03-02 |
Genre | : Computers |
ISBN | : 1107168430 |
This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
Author | : Ljubomir Lalov Ivanov |
Publisher | : |
Total Pages | : 268 |
Release | : 1986 |
Genre | : Recursion theory |
ISBN | : |
Author | : Hartley Rogers |
Publisher | : |
Total Pages | : 526 |
Release | : 1967 |
Genre | : Mathematics |
ISBN | : |
Author | : Stephen Cole Kleene |
Publisher | : |
Total Pages | : 560 |
Release | : 2012-07-01 |
Genre | : |
ISBN | : 9781258442460 |