2.5.2 Incomparable hyperdegrees
We apply the Gandy Basis Theorem to construct a pair of incomparable hyperdegrees.
Lemma 2.5.4. If A is a 
-set containing a nonhyperarithmetic real, then A is uncountable.
Proof. Suppose that A is a countable -set containing a nonhyperarithmetic real. Then the set B = {x ∈ A | x ≰h 
} is a nonempty -subset of A. Hence there ...
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