The Medvedev and Muchnik lattices are an attempt to capture the
computational content of proofs in intuitionistic logic using a 'calculus
of problems'. While the lattices themselves turn out to fall short,
Skvortsova remarkably showed that there exist factors of the Medvedev
lattice which do capture intuitionistic propositional logic (IPC), while
Sorbi and Terwijn later showed the analogous result for the Muchnik
lattice. Unfortunately these factors are constructed in an ad hoc manner
and do not have a clear computational motivation. In this talk I will
present natural factors of the Muchnik lattice which capture IPC, using
well-known concepts such as lowness, 1-genericity, hyperimmune-freeness
and computable traceability.