
Computable Structures and the Hyperarithmetical Hierarchy: Volume 144
Published on 16. June 2000
Book
Hardback
366 pages
978-0-444-50072-4 (ISBN)
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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).
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Elsevier Science & Technology
Target group
Professional and scholarly
Product notice
Laminated cover
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 21 mm
Weight
686 gr
ISBN-13
978-0-444-50072-4 (9780444500724)
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Schweitzer Classification
Persons
Content
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.