The Existence of Minimal Honest Polynomial Degree Below and Recursively Enumerable Degrees

In [1] Homer introduced the honest polynomial reducibility and proved that under this new reducibility a set of minimal degree below 0. is constructed under the assumption that P=NP. In this paper we will prove that under the same assumption a set of minimal degree can be constructed below any recursively enumerable degrees. So under the honest polynomial reducibility a set of low minimal degree does exist.