Inspired by the study of generic and coarse computability of sets, based on the notion of asymptotic density and introduced in computability theory by C.\ Jockusch and P.\ Schupp, our goal is to extend such investigation to the context of computable model theory. We have recently introduced and studied the notions of generically and coarsely computable structures and their generalizations, focusing on equivalence structures and directed graphs induced by one-to-one functions. There are two directions in which these notions of densely computable structures could potentially trivialize: either all structures have a densely computable copy, or only those having a computable (or computably enumerable) copy. We also consider the notions of generically and coarsely computable isomorphisms and their weaker variants. We demonstrate that each notion of a generically or a coarsely computable isomorphism
gives us an interesting insight into the structures. Other topics under investigation include notions of dense computability for abelian groups, models of Peano arithmetic, and effectively closed sets.
Densely Computable Structures And Isomorphisms Pt I
