The undecidable : basic papers on undecidable propositions, unsolvable problems and computable functions

New York : Raven Press, 1965

Abstract/Sommario: This book is an anthology of fundamental papers dealing with undecidability and unsolvability. It begins with Godel's epoch-making paper of 1931 in which it was shown for the first time that systems of logic, no matter how powerful, could never admit proofs of all true assertions of arithmetic. In the anthology, there are the basic papers of Godel, Church, Turing, and Post in which the class of recursive functions was singled out and seen to be just the class of functions that can be c ...; [leggi tutto] This book is an anthology of fundamental papers dealing with undecidability and unsolvability. It begins with Godel's epoch-making paper of 1931 in which it was shown for the first time that systems of logic, no matter how powerful, could never admit proofs of all true assertions of arithmetic. In the anthology, there are the basic papers of Godel, Church, Turing, and Post in which the class of recursive functions was singled out and seen to be just the class of functions that can be computed by finite algorithms. Also included is the work of Church, Turing, and Post in which problems from the theory of abstract computing machines, from mathematical logic, and finally from algebra are shown to be unsolvable in the sense that there is no finite algorithm for dealing with them. Finally, included in the anthology is work of Kleene and of Post initiating the classification theory of unsolvable problems.
Most of the papers collected here have been preyiously available— but only in the periodicals in which they originally appeared. However, it has fortunately also been possible to include previously unpublished lectures by Godel and a hitherto unpublished account by Post of his early work in this area.
This collection should prove valuable, not only as a reference work for specialists, but also as a text or supplementary text: it could be used as a supplementary text in courses in logic or in philosophy or foundations of mathematics. An instructor who prefers to work with original sources could design a course in advanced logic or recursive function theory around this book in various ways. It should also be useful for self-study. With these possibilities in mind, I have prefaced most of the papers in this anthology with brief editorial remarks. In these, I aim to tell the student what I would have liked to have been told before reading the paper in question.
Thanks are due to the authors and publishers who have kindly permitted us to reprint these papers. I am especially grateful to Professors Godel and Kleene who have furnished supplementary material to be included with their papers. Finally, it is a pleasure to thank Alan M. Edelson of Raven Press for his patience and cooperation. [comprimi]

Copertina The undecidable : basic papers on undecidable propositions, unsolvable problems and computable functions

Dettagli

Campo	Valore
Descrizione	The undecidable : basic papers on undecidable propositions, unsolvable problems and computable functions / edited by Martin Davis. - New York : Raven Press, 1965. - 440 p. ; 25 cm
Numeri	ISBN: 0911216014
Autori	Davis, Martin - [Responsabilità secondaria]
Chiavi	Logica Matematica
Luogo di pubblicazione	New York - [Luogo di pubblicazione]
Editore	Raven Press - [Editore]
Categorie	Categorie _MONOGRAFIE - LC (Libri dal 1840 fino agli anni '70)
Paese	Stati Uniti
Lingua	Inglese
ID scheda	43675