论文标题
薄$π_1^0 $类和通用学位的成员
members of thin $Π_1^0$ classes and generic degrees
论文作者
论文摘要
如果每个$π^{0} _ {0} _ {1} $ subclass $ q $ $ p $ a $π^{0} _ {1} $ class $ p $都是薄的。 1993年，Cenzer，Downey，Jockusch和Shore启动了对薄薄$π^{0} _ {1} $类的Turing度的研究，并证明没有包含薄$ $π^{0} _ {1} $类的成员的学位可以是缩回的，并且可以递归地概述，并且可以是$ bf的$ bf。在本文中，我们从通用性方面进行了研究，并证明所有2代学位都不包含薄$π^{0} _ {1} $ class的成员。与此相反，我们表明{\ bf 0} $'$下方所有1代学度都包含薄$π^{0} _ {1} $ class的成员。
A $Π^{0}_{1}$ class $P$ is thin if every $Π^{0}_{1}$ subclass $Q$ of $P$ is the intersection of $P$ with some clopen set. In 1993, Cenzer, Downey, Jockusch and Shore initiated the study of Turing degrees of members of thin $Π^{0}_{1}$ classes, and proved that degrees containing no members of thin $Π^{0}_{1}$ classes can be recursively enumerable, and can be minimal degree below {\bf 0}$'$. In this paper, we work on this topic in terms of genericity, and prove that all 2-generic degrees contain no members of thin $Π^{0}_{1}$ classes. In contrast to this, we show that all 1-generic degrees below {\bf 0}$'$ contain members of thin $Π^{0}_{1}$ classes.
