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).
General
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