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 [122]). 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 ...
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