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 G del'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.
General
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