Semirecursive Sets and Positive Reducibility

Semirecursive Sets and Positive Reducibility

Weakly Semirecursive Sets and r.e. Orderings

Kummer, M. and F. Stephan, Weakly semirecursive sets and r.e. orderings, Annals of Pure and Applied Logic 60 (1993) 133-150. Weakly semirecursive sets have been introduced by Jockusch and Owings (1990). In the present paper their investigation is pushed forward by utilizing r.e. partial orderings, which turn out to be instrumental for the study of degrees of subclasses of weakly semirecursive s...

Schnorr trivial sets and truth-table reducibility

We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr triviality based on truth-table reducibility. These characterizations allow us to see not only that some natural classes of sets, including maximal sets, are composed entirely of Schnorr trivials, but also that the Schnorr trivial sets form an ideal in the truth-table degrees but not the weak t...

Computably Enumerable Sets and Quasi-Reducibility

We consider the computably enumerable sets under the relation of Qreducibility. We first give several results comparing the upper semilattice of c.e. Q-degrees, 〈RQ,≤Q 〉, under this reducibility with the more familiar structure of the c.e. Turing degrees. In our final section, we use coding methods to show that the elementary theory of 〈RQ,≤Q 〉 is undecidable.

Relating Equivalence and Reducibility to Sparse Sets

For various polynomial-time reducibilities r, this paper asks whether being r-reducible to a sparse set is a broader notion than being r-equivalent to a sparse set. Although distinguishing equivalence and reducibility to sparse sets, for many-one or 1-truth-table reductions, would imply that P 6= NP, this paper shows that for k-truth-table reductions, k 2, equivalence and reducibility to sparse...