论文标题
关于坚固的最小对的不存在
On the Nonexistence of a Strong Minimal Pair
论文作者
论文摘要
两个非零的递归枚举（R.E.）度$ \ MathBf {a} $和$ \ MathBf {B} $如果$ \ Mathbf {a} \ wedge \ wedge \ Mathbf {b} = \ naterbf {a}对于任何非零R.E.度$ \ Mathbf {X} \ Leq \ Mathbf {a} $。我们证明R.E.没有强大的最小对。学位。我们的构造超出了通常的$ \ mathbf {0}''$ - 优先参数，我们提供一些证据表明它需要$ \ mathbf {0}^{（4）} $ - 优先参数。
Two nonzero recursively enumerable (r.e.) degrees $\mathbf{a}$ and $\mathbf{b}$ form a strong minimal pair if $\mathbf{a} \wedge \mathbf{b}=\mathbf{0}$ and $\mathbf{b}\vee \mathbf{x}\geq \mathbf{a}$ for any nonzero r.e. degree $\mathbf{x}\leq \mathbf{a}$. We prove that there is no strong minimal pair in the r.e. degrees. Our construction goes beyond the usual $\mathbf{0}'''$-priority arguments and we give some evidence to show that it needs $\mathbf{0}^{(4)}$-priority arguments.
