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| COMPUTABLE STRUCTURES AND THE HYPERARITHMETICAL HIERARCHY, 144
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By
C.J. Ash
J. Knight, University of Notre Dame, Department of Mathematics, Notre Dame, IN, USA
Included in series
Studies in Logic and the Foundations of Mathematics, 144
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).
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. α-systems. Back-and forth relations. Theorems
of Barker and Davey. Pairs of computable structures. Models of arithmetic. Special classes of structures.
Bibliographic & ordering Information
Hardbound, 366 pages, publication date: JUN-2000
ISBN-13: 978-0-444-50072-4
ISBN-10: 0-444-50072-3
Imprint: ELSEVIER
Price: Order form
GBP 78
EUR 117
USD 133
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Last update: 29 Aug 2008
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