论文标题
在分离类中实现计算的枚举学位
Realizing Computably Enumerable Degrees in Separating Classes
论文作者
论文摘要
我们调查了哪些C.E. \ Turing学位的集合可以实现为分离$π^0_1 $ c.e. \ guger类的元素的集合。我们表明，对于每个C.E. \ guger $ \ MathBf {C} $，Collection $ \ {\ MathBf {C}，\ Mathbf {0}'\} $可以实现。我们还排除了几项尝试构建分离类的尝试，以实现独特的c.e. \度。例如，我们表明没有\ emph {super-maximal}对：diss c.e. \ set $ a $ a $ a $ and $ b $，其分离类是无限的，但是C.E. \ guger的每个分离器都是$ a $ a $ a $ a $ a $ a $ a $ a $ a或$ \ overline {b} $的有限变体。
We investigate what collections of c.e.\ Turing degrees can be realised as the collection of elements of a separating $Π^0_1$ class of c.e.\ degree. We show that for every c.e.\ degree $\mathbf{c}$, the collection $\{\mathbf{c}, \mathbf{0}'\}$ can be thus realized. We also rule out several attempts at constructing separating classes realizing a unique c.e.\ degree. For example, we show that there is no \emph{super-maximal} pair: disjoint c.e.\ sets $A$ and $B$ whose separating class is infinite, but every separator of c.e.\ degree is a finite variant of either $A$ or $\overline{B}$.
