{"id":"openai-math/Rigidity-of-the-Turing-degrees","pdf":"https://github.com/openai/math/blob/main/preprints/Rigidity-of-the-Turing-degrees-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Rigidity-of-the-Turing-degrees-September-24-2026","tags":["computability","turing-degrees","order-theory"],"score":0,"title":"Rigidity of the Turing degrees","domain":"Mathematical logic","family":"241","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.LO","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://blog.computationalcomplexity.org/2026/10/conjecture-that-i-thought-would-not-be.html#:~:text=6%29%20Is%20there%20a%20non%2Dtrivial%20automorphism%20of%20the%20Turing%20degrees","kind":"web","site":"blog.computationalcomplexity.org","text":"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…","added":"2026-11-03","title":"Conjectures that I thought would not be proved in my lifetime....were","author":"Bill Gasarch"}],"formalized":true,"family_title":"Rigidity of the Turing degrees"}