Definability and Computability / Edition 1

by Yuri L. Ershov

Overview

In this book, Yurii L. Ershov posits the view that computability-in the broadest sense-can be regarded as the Sigma-definability in the suitable sets. He presents a new approach to providing the Gödel incompleteness theorem based on systematic use of the formulas with the restricted quantifiers. The volume also includes a novel exposition on the foundations of the theory of admissible sets with urelements, using the Gandy theorem throughout the theory's development. Other topics discussed are forcing, Sigma-definability, dynamic logic, and Sigma-predicates of finite types.

Product Details

ISBN-13:	9780306110399
Publisher:	Springer US
Publication date:	04/30/1996
Series:	Siberian School of Algebra and Logic
Edition description:	1996
Pages:	264
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

Sigmadefinability and the Gödel Incompleteness Theorem. Computability on Admissible Sets. Selected Topics. Appendix. Index.

Editorial Reviews

Offers a proof of the Godel incompleteness theorem based on applying the notion of a zeta-definable function as a specification of the notion of a computable function on natural numbers; introduces the theory of computability on an arbitrary admissible set with urelements; and surveys a number of selected issues regarding compatibility in admissible sets. Does not discuss the authorship of the ideas and methods, but does divide the bibliography into primary and secondary sources. Published simultaneously in Russian by Scientific Books in Novosibirsk. Distributed in the US by Plenum. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews