Ebook: Recursive Functions and Metamathematics: Problems of Completeness and Decidability, Gödel’s Theorems
Author: Roman Murawski (auth.)
- Tags: Logic, Mathematical Logic and Foundations, Philosophy of Science, Theory of Computation
- Series: Synthese Library 286
- Year: 1999
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages i-xii
Introduction....Pages 1-17
Recursive Functions....Pages 19-95
G?del’s Incompleteness Theorems....Pages 97-210
Decidability Theory....Pages 211-280
Philosophical Comments....Pages 281-340
Back Matter....Pages 341-395
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.
Content:
Front Matter....Pages i-xii
Introduction....Pages 1-17
Recursive Functions....Pages 19-95
G?del’s Incompleteness Theorems....Pages 97-210
Decidability Theory....Pages 211-280
Philosophical Comments....Pages 281-340
Back Matter....Pages 341-395
....