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

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

 

Synopses & Reviews

Publisher Comments:

"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.

Book News Annotation:

In this corrected reprint of the work originally published by Raven Press Books, Ltd., Hewlett, New York, in 1965, Davis (emeritus, mathematical sciences, New York U.) collects classic papers and authors' supplementary notes tackling undecidability and unsolvability. The anthology begins with G<:o>del's landmark 1931 paper arguing that formal logic systems cannot admit proofs of all true assertions of arithmetic. Church, Turing, Post, and Kleene treat recursive functions, problems from the theory of abstract computing machines, and the classification theory of unsolvable problems.
Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

An anthology of fundamental papers on undecidability and unsolvability, this classic reference opens with G&ouml;del's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by G&ouml;del, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. 1965 edition.

Synopsis:

An anthology of papers on undecidability and unsolvability by major figures, this reference is suited as a text for graduate and undergraduate courses in logic, philosophy, and foundations of mathematics. Slightly corrected republication of the edition published by Raven Press Books, Ltd., Hewlett, New York, 1965.

About the Author

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." &#8212; 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." &#8212; The Review of Metaphysics

"Much more than a mere collection of papers . . . a valuable addition to the literature." &#8212; Mathematics of Computation

Table of Contents

Kurt G&ouml;del: On Formally Undecidable Propositions of the Principia Mathematica and Related Systems; On Undecidable Propositions of Formal Mathematical Systems, On Intuitionistic Arithmetic and Number Theory, On the Length of Proofs, Remarks Before the Princeton Bicentennial Conference of Problems in Mathematics

Alonzo Church: An Unsolvable Problem of Elementary Number Theory, A Note on the Entscheidungsproblem

Alan M. Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Systems of Logic Based on Ordinals

J. B. Rosser: An Informal Exposition of Proofs of G&ouml;del's Theorem and Church's Theorem, Extensions of Some Theorems of G&ouml;del and Church

Stephen C. Kleene: General Recursive Functions of Natural Numbers, Recursive Predicates and Quantifiers

Emil Post: Finite Combinatory Processes, Formulation I; Recursive Unsolvability of a Problem of Thue, Recursively Enumerable Sets of Positive Integers and Their Decision Problems, Absolutely Unsolvable Problems and Relatively Undecidable Propositions—Account of an Anticipation.

Index.

Product Details

ISBN:
9780486432281
Editor:
Davis, Martin
Publisher:
Dover Publications
Editor:
Davis, Martin
Author:
Davis, Martin
Author:
Mathematics
Location:
Mineola, NY
Subject:
General
Subject:
Logic
Subject:
Computable functions
Subject:
Recursive functions
Subject:
Gèodel's theorem.
Subject:
Turing machines.
Subject:
Unsolvability
Subject:
General Mathematics
Subject:
Mathematics-Logic and Philosophy
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
Nr. 92
Publication Date:
20040231
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
414
Dimensions:
1400x1800

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The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions New Trade Paper
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Product details 414 pages Dover Publications - English 9780486432281 Reviews:
"Synopsis" by ,
An anthology of fundamental papers on undecidability and unsolvability, this classic reference opens with G&ouml;del's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by G&ouml;del, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. 1965 edition.

"Synopsis" by , An anthology of papers on undecidability and unsolvability by major figures, this reference is suited as a text for graduate and undergraduate courses in logic, philosophy, and foundations of mathematics. Slightly corrected republication of the edition published by Raven Press Books, Ltd., Hewlett, New York, 1965.
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