Minimal pairs of polynomial degrees with subexponential complexity

Constructing Minimal Pairs of Degrees

We prove that there exist sets of natural numbers A and B such that A and B form a minimal pair with respect to Turing reducibility, enumeration reducibility, hyperarithmetical reducibility and hyperenumer-ation reducibility. Relativized versions of this result are presented as well. 1. Introduction In the present paper we consider four kinds of reducibilities among sets of natural numbers: Tur...

Minimal Degrees for Honest Polynomial Reducibilities

The existence of minimal degrees is investigated for several polynomial reducibilities. It is shown that no set has minimal degree with respect to polynomial many-one or Turing reducibility. This extends a result. of Ladner [L] whew reciirsive sets are considered. An "honest '' polynomial reducibility, < ; , is defined which is a strengthening of polynomial Turing reduc-ibility. We prove that n...

The Complexity of the Minimal Polynomial

Bounding and nonbounding minimal pairs in the enumeration degrees

We show that every nonzero ∆ 2 e-degree bounds a minimal pair. On the other hand, there exist Σ 2 e-degrees which bound no minimal pair.

Minimal Pairs and Quasi-minimal Degrees for the Joint Spectra of Structures

Two properties of the Co-Spectrum of the Joint Spectrum of finitely many abstract structures are presented a Minimal Pair type theorem and the existence of a Quasi-Minimal degree with respect to the Joint Spectrum of the structures.