The Undecidable: Basic Papers on Undecidable Propostions, Unsolvable Problems and Computable Functions (Dover Books on Mathematics)

Book Details

• Author: Martin Davis

• Brand: Dover

• Edition: Illustrated

• Binding: Paperback

• Format: Illustrated

• Number of Pages: 416

• Release Date: 18-02-2004

• Languages: English

• ISBN: 9780486432281

About the Book

This anthology presents a collection of fundamental papers on undecidability and unsolvability, penned by key figures in the field. It serves not only as an invaluable source of original materials but also as a historical reference that outlines current problems in the domains of logic, mathematics, and philosophy. This classic reference work is ideal for graduate and undergraduate courses in logic, philosophy, and the foundations of mathematics, and also serves as an excellent resource for self-study.

The volume opens with Kurt Gödel's landmark 1931 paper, which established that systems of logic cannot prove all true assertions of arithmetic. It then includes seminal works by Gödel, Alonzo Church, Alan Turing, and Emil Post, each contributing to the concept of recursive functions and the limitations of computability by finite algorithms. The papers explore unsolvable problems in the theory of abstract computing machines, mathematical logic, and algebra. Additionally, works by Church, Turing, and Post cover the notion of unsolvable problems, while contributions by Kleene and Post introduce the classification theory of unsolvable problems.

The book also includes corrections, emendations, and added commentaries by Gödel, Church, and Kleene, making it a comprehensive and insightful resource for those interested in the historical and theoretical development of the field.