Intuitionistic logic and Muchnik degrees

We prove that there is a factor of the Muchnik lattice that captures intuitionistic propositional logic. This complements a now classic result of Skvortsova for the Medvedev lattice

Friedberg numberings in the Ershov hierarchy

We show that for every n 1, there exists a 1n -computable family which up to equivalence has exactly one Friedberg numbering which does not induce the least element of the corresponding Rogers semilattice