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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