Subsets of hypersimple sets
Rodney G. Downey · Pacific Journal of Mathematics · 1987
Structural properties of r.e.sets often have degree theoretic consequences, particularly concerning degrees of supersets.It is our intention to show that such properties can have interesting ramifications on the degrees of subsets, by showing that no hypersimple r.e.set has the universal splitting property (USP).We also show that there are, however, simple sets (indeed, low and promptly simple sets) with USP and thus USP is not invariant under automorphisms of the lattice of r.e.sets.