Recursive Functions and Metamathematics
Recursive Functions and Metamathematics

Author: Roman Murawski

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 416

ISBN-13: 9401728666

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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.

Recursion Theory for Metamathematics
Recursion Theory for Metamathematics

Author: Raymond M. Smullyan

Publisher: Oxford University Press, USA

Published: 1993

Total Pages: 180

ISBN-13: 019508232X

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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.

Recursive Analysis
Recursive Analysis

Author: R. L. Goodstein

Publisher: Courier Corporation

Published: 2013-01-23

Total Pages: 213

ISBN-13: 0486158152

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This text by a master in the field covers recursive convergence, recursive and relative continuity, recursive and relative differentiability, the relative integral, elementary functions, and transfinite ordinals. 1961 edition.