Computable Structures and the Hyperarithmetical Hierarchy

Computable Structures and the Hyperarithmetical Hierarchy

1st Edition - May 1, 2000

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  • Authors: C.J. Ash, J. Knight
  • eBook ISBN: 9780080529523

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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).

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.

Product details

  • No. of pages: 366
  • Language: English
  • Copyright: © Elsevier Science 2000
  • Published: May 1, 2000
  • Imprint: Elsevier Science
  • eBook ISBN: 9780080529523

About the Authors

C.J. Ash

J. Knight

Affiliations and Expertise

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

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