Automorphism Problem for the Turing Degrees

Determine the automorphism group of the partial order of Turing degrees.

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Claimed by OpenAI.

every order automorphism of the full partial order of Turing degrees is the identity, in ZFC and without definability or regularity assumptions.

Repository: https://github.com/openai/math

Manuscript: https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Rigidity-of-the-Turing-degrees-September-24-2026/paper.pdf

  • OpenAI-241-01-Rigidity-of-the-Turing-degrees.pdf294,854 bytesOpen