Title: Computable Structures and the Hyperarithmetical Hierarchy (Volume 144) (Studies in Logic and the Foundations of Mathematics, Volume 144)
Publisher: Elsevier Science
Publication Date: 2000
Language: English
ISBN 10: 0444500723
ISBN 13: 9780444500724
Binding: Hardcover
Condition: New

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Synopsis

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).

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