Recursive Functions and Metamathematics

Problems of Completeness and Decidability, Gödel’s Theorems

Nonfiction, Science & Nature, Mathematics, Logic, Religion & Spirituality, Philosophy
Cover of the book Recursive Functions and Metamathematics by Roman Murawski, Springer Netherlands
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Author: Roman Murawski ISBN: 9789401728669
Publisher: Springer Netherlands Publication: March 14, 2013
Imprint: Springer Language: English
Author: Roman Murawski
ISBN: 9789401728669
Publisher: Springer Netherlands
Publication: March 14, 2013
Imprint: Springer
Language: English

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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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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