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Rigidity of the Turing degrees
Every order automorphism of the Turing degrees is the identity, resolving their rigidity problem. Thus no nontrivial relabeling of degrees preserves the ordering by relative computability.
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Rigidity of the Turing degrees
Sep 24, 2026·paper.pdfLean
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.