Recursive Functions and Metamathematics

Problems of Completeness and Decidability, G¶del's Theorems

By: Roman Murawski

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Hardcover | 30 September 1999

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412 Pages

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23.5 x 15.88 x 3.18

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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 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.

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Preface
Introduction	p. 1
Recursive Functions	p. 19
Computable Functions	p. 19
Recursive Functions	p. 21
Markov Algorithms and Turing Machines	p. 39
Primitive and Elementary Recursive Functions	p. 51
Arithmetical Hierarchy	p. 75
Church's Thesis	p. 84
Historical Remarks	p. 90
Godel's Incompleteness Theorems	p. 97
Arithmetic of Natural Numbers	p. 97
Representability in Peano Arithmetic	p. 103
Arithmetization of Syntax	p. 116
Godel's Theorems	p. 127
Paris-Harrington and Paris-Kirby Theorems	p. 157
Satisfaction and Consistency	p. 173
Historical Remarks	p. 196
Decidability Theory	p. 211
Basic notions and theorems	p. 211
Decidable Theories	p. 217
Undecidable Theories	p. 245
Historical Remarks	p. 275
Philosophical Comments	p. 281
Direct Consequences of Godel's Results	p. 281
Godel's Theorems vs. Hilbert's Program	p. 303
Generalized Hilbert's Program	p. 311
Relativized Hilbert's Program vs. Reverse Mathematics	p. 314
Hilbert's Tenth Problem	p. 323
Godel's Theorems and Computer Science	p. 325
Godel's Theorems and General Philosophy	p. 337
Conclusions	p. 338
Bibliography	p. 341
List of Symbols	p. 377
Index	p. 383
Table of Contents provided by Blackwell. All Rights Reserved.

Recursive Functions and Metamathematics

Problems of Completeness and Decidability, G¶del's Theorems

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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