We show that if M is an r-maximal set, A is a major subset of M, B is an arbitrary set and $M\setminus A{\equiv }_{Q_{1,N}}B$, then $M\setminus A{\le }_{m}B$. We prove that the c.e. $Q_{1,N}$-degrees are not dense. We also show that there exist infinite collections of $Q_{1,N}$-degrees ${\{{\mathbf{a}}_i\}}_{i\in \omega }$ and ${\{{\mathbf{b}}_j\}}_{j\in \omega }$ such that the following hold: (i) for every i, j, ${\mathbf{a}}_i{<}_{Q_{1,N}}{\mathbf{a}}_{i+1}$, ${\mathbf{b}}_{j+1}{<}_{Q_{1,N}}{\mathbf{b}}_j$ and ${\mathbf{a}}_i{<}_{Q_{1,N}}{\mathbf{b}}_j$,

中文翻译：

---

r-Maximal 集和 Q1,N-可约性

我们证明如果M是一个r极大集，A是M的主要子集，B是一个任意集，并且$米\setminus \mathrm{一种}{\equiv }_{{问}_{1,N}}乙$， 然后 $米\setminus \mathrm{一种}{\le }_{米}乙$. 我们证明 ce${问}_{1,N}$-度数不密集。我们还表明存在无限的集合${问}_{1,N}$-度数 ${\{{\mathbf{一种}}_{\mathrm{一世}}\}}_{\mathrm{一世}\in \omega }$ 和 ${\{{\mathbf{乙}}_j\}}_{j\in \omega }$使得以下成立：（i）对于每个i，j，${\mathbf{一种}}_{\mathrm{一世}}{<}_{{问}_{1,N}}{\mathbf{一种}}_{\mathrm{一世}+1}$, ${\mathbf{乙}}_{j+1}{<}_{{问}_{1,N}}{\mathbf{乙}}_j$ 和 ${\mathbf{一种}}_{\mathrm{一世}}{<}_{{问}_{1,N}}{\mathbf{乙}}_j$,