Computable Structures and the Hyperarithmetical Hierarchy

by C.J. Ash, J.F. Knight

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).

366 pages, Hardcover

First published May 1, 2000

Reviews

[Sheffielder · Rating 4 out of 5]

An excellent source book for researchers. Some simply-explained examples would be helpful, e.g. a basic example of a set that is hyperarithmetical but not arithmetical.