Recursive Functions and Metamathematics
Subtitle: Problems of Completeness and Decidability, Gödel's Theorems
By: by Roman Murawski
Series: Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science -- 286; Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science -- 286
Publisher: Springer Netherlands
Published: 1999
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 395
ISBN-13: 9789048152988; 9789401728669
Subjects: Philosophy; Philosophy (General); Symbolic and mathematical Logic; Logic; Science; Information theory
Description: 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.
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