The Undecidable Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions

by Davis, Martin

• ISBN13: 9780486432281
• ISBN10: 0486432289
• Format: Paperback
• Copyright: 2004-02-18
• Publisher: Dover Publications

Summary

"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 ComputationAn anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Gödel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by Gödel, 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. Suitable for graduate and undergraduate courses. 1965 ed.

Author Biography

Martin Davis: Computer Science Pioneer
Dover's publishing relationship with Martin Davis, now retired from NYU and living in Berkeley, goes back to 1985 when we reprinted his classic 1958 book Computability and Unsolvability, widely regarded as a classic of theoretical computer science. A graduate of New York's City College, Davis received his PhD from Princeton in the late 1940s and became one of the first computer programmers in the early 1950s, working on the ORDVAC computer at The University of Illinois. He later settled at NYU where he helped found the Computer Science Department.

Not many books from the infancy of computer science are still alive after several decades, but Computability and Unsolvability is the exception. And The Undecidable is an anthology of fundamental papers on undecidability and unsolvability by major figures in the field including Godel, Church, Turing, Kleene, and Post.

Critical Acclaim for Computability and Unsolvability:
"This book gives an expository account of the theory of recursive functions and some of its applications to logic and mathematics. It is well written and can be recommended to anyone interested in this field. No specific knowledge of other parts of mathematics is presupposed. Though there are no exercises, the book is suitable for use as a textbook." — J. C. E. Dekker, Bulletin of the American Mathematical Society, 1959

Critical Acclaim for The Undecidable:
"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

Table of Contents

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
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