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 ComputationAn 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
Country of Publication:
Series: Dover Books on Mathematics
18 February 2004
Kurt Godel: On Formally Undecidable Propositions of the Principia Mathematica and Related Systems; On Undecidable Propositions of Formal Mathematical Systems, On Intuitionistic Arithmetic and Number Theory, On the Length of Proofs, Remarks Before the Princeton Bicentennial Conference of Problems in Mathematics Alonzo Church: An Unsolvable Problem of Elementary Number Theory, A Note on the Entscheidungsproblem Alan M. Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Systems of Logic Based on Ordinals J. B. Rosser: An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem, Extensions of Some Theorems of Godel and Church Stephen C. Kleene: General Recursive Functions of Natural Numbers, Recursive Predicates and Quantifiers Emil Post: Finite Combinatory Processes, Formulation I; Recursive Unsolvability of a Problem of Thue, Recursively Enumerable Sets of Positive Integers and Their Decision Problems, Absolutely Unsolvable Problems and Relatively Undecidable Propositions-Account of an Anticipation. Index.