Abstract:
One of the central topics in computable algebra and model theory is concerned with the study of
computable isomorphisms. Classically, we do not distinguish between isomorphic structures, however, from
computability point of view, isomorphic structures can differ quite dramatically. A typical example is
provided by the linear order of type ω. It has two computable copies such that in one the successor function
is computable, but it is not computable in the other. These are clearly classically isomorphic, but they are
not computably isomorphic.