Nonuniversality conjecture for recursive isomorphism on $2^\omega$

Equivalent formulations 1

Other statements of this same problem, merged from separate entries. Each is equivalent to the statement above — proving any one settles them all.

1. Nonuniversality conjecture for recursive isomorphism on $2^\omega$

   Let $2^\omega$ be Cantor space. Recursive isomorphism on $2^\omega$ is the countable Borel equivalence relation identifying two elements when they are recursively isomorphic.

   Nonuniversality conjecture. Recursive isomorphism on $2^\omega$ is not a universal countable Borel equivalence relation.

   Recursive isomorphism on $2^\omega$ is known to be measure universal, but its universality remains unresolved; the conjecture asserts that measure universality does not extend to universality.

   source: Andrew S Marks, “Uniformity, Universality, and Computability Theory”, arXiv:1606.01976 (2017).