Undecidable

Basic Papers on Undecidable Propostions, Unsolvable Problems and Computable Functions

By: MARTIN DAVIS

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Paperback | 18 February 2004

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"A valuable collection both for original source material as well as historical formulations of current problems." — The Review of Metaphysics
"Much more than a mere collection of papers. A valuable addition to the literature." — Mathematics of Computation
An anthology of fundamental papers on undecidability and unsolvability by major figures in the field , this classic reference is ideally suited as a text for graduate and undergraduate courses in logic, philosophy, and foundations of mathematics. It is also appropriate for self-study.
The text opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems.
Supplementary items include corrections, emendations, and added commentaries by Godel, Church, and Kleene for this volume's original publication, along with a helpful commentary by the editor.

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On Formally Undecidable Propositions of the Principia Mathematica and Related Systems. I	p. 4
On Undecidable Propositions of Formal Mathematical Systems	p. 39
On Intuitionistic Arithmetic and Number Theory	p. 75
On the Length of Proofs	p. 82
Remarks Before the Princeton Bicentennial Conference on Problems in Mathematics	p. 84
An Unsolvable Problem of Elementary Number Theory	p. 88
A Note on the Entscheidungsproblem	p. 108
On Computable Numbers, with an Application to the Entscheidungsproblem	p. 115
Systems of Logic Based on Ordinals	p. 154
An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem	p. 223
Extensions of Some Theorems of Godel and Church	p. 230
General Recursive Functions of Natural Numbers	p. 236
Recursive Predicates and Quantifiers	p. 254
Finite Combinatory Processes. Formulation I	p. 288
Recursive Unsolvability of a Problem of Thue	p. 292
Recursively Enumerable Sets of Positive Integers and Their Decision Problems	p. 304
Absolutely Unsolvable Problems and Relatively Undecidable Propositions- Account of an Anticipation	p. 338
Index	p. 434
Table of Contents provided by Rittenhouse. All Rights Reserved.

Undecidable

Basic Papers on Undecidable Propostions, Unsolvable Problems and Computable Functions

At a Glance

Paperback

Shipping

How to return your order

Defective items

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