The Undecidable by Martin Davis

The Undecidable by Martin Davis

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.

Martin Davis, a renowned prize-winning logician, has dedicated more than six decades of his life to the crucial intersection of logic and computer science. He was born in New York City and obtained his Ph.D. from Columbia University. In 1950, he graduated from Princeton University. He worked for thirty years at New York University, where he was instrumental in the establishment of the computer science department. His knowledge, combined with his genuine enthusiasm for the subject and exceptional narrative skills, make him the ideal person to tell this story. Professor Davis is now Professor Emeritus at New York University and resides in Berkeley, California, with his 66-year-old wife.