Non-recursive enumerability for effective models in continuous semantics

Let $\mathscr{M}$ be an effective model of the $bb$-calculus living in Scott's continuous semantics, and write $Th(\mathscr{M})$ for its equational theory.

Continuous-semantics conjecture. All the effective models living in the continuous semantics have non-r.e. equational theories.

The paper presents this as the strongest of the listed open instances of the Scott-semantics conjecture. It is not settled by the results proving the analogous assertion for stable and strongly stable semantics.