Computable Transformations of Structures

Abstract

The isomorphism problem, for a class of structures, is the set of pairs of structures within that class which are isomorphic to each other. Isomorphism problems have been well studied for many classes of computable structures. Here we consider isomorphism problems for broader classes of countable structures, using Turing functionals and applying the notions of finitary and countable computable reductions which have been developed for equivalence relations more generally.