members of thin ${\Pi }_1^0$ classes and generic degrees

Frank Stephan, Guohua Wu, Bowen Yuan

A ${\Pi }_1^0$ class $P$ is thin if every ${\Pi }_1^0$ subclass $Q$ of $P$ is the intersection of $P$ with some clopen set. In 1993, Cenzer, Downey, Jockusch and Shore initiated the…