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Recursion Theory by Liang Yu, Chi Tat Chong

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10 Rigidity and biinterpretability of hyperdegrees

Let 〈imageh, ≤〉 denote the structure of hyperdegrees under the partial ordering ≤ for hyperarithmetic reducibility. As for the Turing degrees 〈image, ≤〉, the hyperdegrees form an upper semilattice under the join operator ∪, where if the hyperdegrees of x and y are respectively a and b, then xy has hyperdegree ab. Note that ∪ may be defined in terms of ≤. A map of image or h into itself is an automorphism if ...

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