A Open problems
A.1 Hyperarithmetic theory
We first list a question which has remained open for almost 40 years.
Question A.1.1 (Sacks ). Does every countable set of hyperdegrees have a minimal upper bound?
The next question concerns a version of the Posner–Robinson Theorem in the hyperarithmetic setting.
Question A.1.2. Let x ∉ HYP and let A ⊆ 2ω be and uncountable. Is there a y ∈ A such that x ⊕ y ≥h ?
A.2 Set-theoretic problems in recursion theory
The most important problem in this area is probably Martin’s Conjecture (6.6.9). We also have ...