Arithmetical Sacks forcing (Q2505505)

The authors construct a hyperimmune-free minimal degree below a 1-generic degree, thereby settling a question posed by Jockusch. In fact, they indicate how to accomplish this so that the degrees lie below \(\mathbf{0''}\). The paper's title refers to the construction method they introduce, which is based on computable perfect trees. They also show that, in contrast, there exists a hyperimmune-free degree \(\mathbf m\) not below any 1-generic degree, and they sketch a proof that \(\mathbf m\) may even be chosen to be minimal and below \(\mathbf{0''}\).