On bounded m-reducibilities

Abstract

Conditions for classes F1, F0 of non-decreasing total one-place arithmetic functions to define reducibility m [R1 R0 ] {(A,B)|A,B N & (9 r.f. h)(9f1 2 F1)(9f0 2 F0) [A h m B & f0 E h E f1]} where k E l means that function l majors function k almost everywhere are studied. It is proved that the system of these reducibilities is highly ramified, and examples are constructed which differ drastically m [R1 R0 ] from the standard m-reducibility with respect to systems of degrees. Indecomposable and recursive degrees are considered.