Recursive Functions and Metamathematics Problems of Completeness and Decidability, Godel's Theorums

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.Murawski, Roman is the author of 'Recursive Functions and Metamathematics Problems of Completeness and Decidability, Godel's Theorums', published 1999 under ISBN 9780792359043 and ISBN 0792359046.