7.3.2 A transfinite Posner–Robinson Theorem
Theorem 7.3.1 may be iterated into the transfinite in several different ways. Here is the first version.
Theorem 7.3.2. (Slaman and Steel [142]). Let 0 < 
and let z be a real such that 
(γ) <T z for each γ<β. Then there is a g such that g ⊕ z ≡T g(β).
The rest of the section is devoted to a proof of Theorem 7.3.2.
Let a ∈ 
. The first step is to introduce an enumeration of arithmetical predicates indexed by ...
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