Computable Structures and the Hyperarithmetical Hierarchy, Volume 144

1st Edition

Authors: C.J. Ash J. Knight
Hardcover ISBN: 9780444500724
eBook ISBN: 9780080529523
Imprint: Elsevier Science
Published Date: 16th June 2000
Page Count: 366
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Table of Contents

Preface. Computability. The arithmetical hierarchy. Languages and structures. Ordinals. The hyperarithmetical hierarchy. Infinitary formulas. Computable infinitary formulas. The Barwise-Kreisel Compactness Theorem. Existence of computable structures. Completeness and forcing. The Ash-Nerode Theorem. Computable categoricity and stability. n-systems. &agr;-systems. Back-and forth relations. Theorems of Barker and Davey. Pairs of computable structures. Models of arithmetic. Special classes of structures.

Description

This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties).


Details

No. of pages:
366
Language:
English
Copyright:
© Elsevier Science 2000
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080529523
Hardcover ISBN:
9780444500724

About the Authors

C.J. Ash Author

J. Knight Author

Affiliations and Expertise

University of Notre Dame, Department of Mathematics, Notre Dame, IN, USA