Affiliations: [a] Department of Mathematics, Iowa State University, Ames, IA, USA. [email protected] | [b] Campus scientifique, Laboratoire lorrain de recherche en informatique et ses applications, BP 239, 54506 Vandoeuvre-lés Nancy Cedex, France. [email protected]
Note:  An abbreviated version of this paper first appeared in the proceedings of the fourteenth Computability in Europe conference.
Abstract: When p is a computable real so that p⩾1, we define the isometry degree of a computable presentation of ℓp to be the least powerful Turing degree d by which it is d-computably isometrically isomorphic to the standard presentation of ℓp. We show that this degree always exists and that when p≠2 these degrees are precisely the c.e. degrees.