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 image and uncountable. Is there a yA such that xyh image?

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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