Recursive Functions and Metamathematics: Problems of Completeness and Decidability, Gödel's Theorems - Couverture rigide

Murawski, Roman

Couverture rigide

ISBN 10 : 0792359046 ISBN 13 : 9780792359043

Editeur : Kluwer Academic Publishers, 1999

Synopsis

Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography.
Readership: Scholars and advanced students of logic, mathematics, philosophy of science.

A propos du livre

Présentation de l'éditeur

An Early History of Recursive Functions and Computability traces the development of recursive functions from their origins in the late nineteenth century, when recursion was first used as a method of defining simple arithmetic functions, up to the mid-1930's, when the class of general recursive functions was introduced by Godel, formalized by Kleene and used by Church in his thesis. The book explains how the proposal given in Church's 1936 paper, now known as Church's thesis, first arose and concludes with the consideration of another class of functions, the Turing computable functions, that were specially created to be equivalent to the class of effectively calculable functions. The book includes previously unpublished letters between the author and many of the key historical figures.

Biographie de l'auteur

Rod Adams received his PhD from the School of Information Sciences at The Hatfield Polytechnique under the supervision of Dr. Dale Johnson. Dr. Adams is currently a Professor of Neural Computation at the University of Hertfordshire.

Détails de l'édition

• Éditeur: Kluwer Academic Publishers
• Date d'édition: 1999
• Langue: anglais
• ISBN 10: 0792359046
• ISBN 13: 9780792359043
• Reliure: Relié
• Nombre de pages: 407
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne