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 Goedel'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.
- ISBN13 9789048152988
- Publish Date 6 December 2010 (first published 30 September 1999)
- Publish Status Active
- Publish Country NL
- Imprint Springer
- Edition Softcover reprint of hardcover 1st ed. 1999
- Format Paperback
- Pages 395
- Language English