Rigidity of the Turing degrees at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Rigidity of the Turing degrees

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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expertly designed by an internal OpenAI model

Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	logic, thinking really hard	Levels:	1
Category:	Mathematical logic	Lean version:	YES! ✔
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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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LEVEL 1 Rigidity of the Turing degrees

released 2026-09-24 | 2 theorems · 4 lemmas · 7 proofs · 4,407 words | PLAY LEVEL 1 » (pdf)

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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