The research goals of this proposal are to address key unresolved questions about the theory of computable numbering and properties of the degree structure of Rogers semilattices, also to study the theory of numbering and degree structures of computable enumerable equivalence relations from the perspective of Reverse Mathematics, which tries to answer questions like this by finding exactly which set-theoretic axioms are truly necessary to prove theorems from theory of numbering and degree structure of ceers. Also, we will study the extension of the domain of numbering and computable enumerable equivalence relations to first uncountable ordinals and punctual settings.