Definability And Computability

Download or read book Definability and Computability written by I︠U︡riĭ Leonidovich Ershov and published by Springer Science & Business Media. This book was released on 1996-04-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.