Rigidity of the Turing degrees
Source: github.com/openai/math/tree/main/preprints/Rigidity-of-the-…
We prove that every order automorphism of the full partial order of Turing degrees is the identity, resolving the rigidity conjecture for the Turing degrees positively.
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Conjectures that I thought would not be proved in my lifetime....wereblog.computationalcomplexity.orgBill Gasarch
6) Is there a non-trivial automorphism of the Turing degrees? Let TD be the set of all Turing degrees. An automorphism of the Turing degrees is a bijection \(f\) from TD to TD such that \( a \le_T b \) if and only if \( f(a) \le_T f(b) \). A non-trivial automorphism is one that is not the identity…