Computable Structures and the Hyperarithmetical Hierarchy

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).Ash, C. J. is the author of 'Computable Structures and the Hyperarithmetical Hierarchy' with ISBN 9780444500724 and ISBN 0444500723.