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

Undecidable: Basic Papers on Problems Propositions Unsolvable Problems and Computable Functions by Davis, Martin. Hardcover edition. ISBN: 9780911216011.

This anthology of fundamental papers dealing with undecidability and unsolvability begins with dels epoch-making paper of 1931. This paper demonstrated for the first time that systems of logic--no matter how powerful--could never admit proofs of all true assertions of arithmetic. Included in this outstanding volume are the basic papers of del, 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 presented 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, the book presents the work of Kleene and of Post initiating the classification theory of unsolvable problems. Already the standard reference work on the subject, The Undecidable is also ideally suited as a text or supplementary text for courses in logic, philosophy, and foundations of mathematics.