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

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Martin Davis
Courier Corporation, 2004 - Mathematics - 413 pages
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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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Contents

On Formally Undecidable Propositions of
4
On Undecidable Propositions of Formal
39
On Intuitionistic Arithmetic and Number Theory
75
On the Length of Proofs
82
An Unsolvable Problem of Elementary Number Theory
88
A Note on the Entscheidungsproblem
108
Systems of Logic Based on Ordinals
154
J B ROSSER
222
Extensions of Some Theorems of Giidel and Church
230
General Recursive Functions of Natural Numbers
236
Recursive Predicates and Quantifiers
254
Finite Combinatory Processes Formulation I
288
Recursively Enumerable Sets of Positive Integers
304
Absolutely Unsolvable Problems and Relatively
338
Index 434
407
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About the author (2004)

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

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