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Rigidity of the Turing degrees

Fixing a cone of degrees or preserving definable operations does not by itself imply that every degree is fixed.

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Understanding the problem

Read the background

Fixing a cone of degrees or preserving definable operations does not by itself imply that every degree is fixed. The target is rigidity of the entire ordering.

The statement concerns the full order of Turing degrees. It should not be transferred to arbitrary degree structures or weaker background theories without an argument.

Why it matters

If correct, extends partial rigidity phenomena to every degree in the full stated ordering.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The statement concerns the full order of Turing degrees. It should not be transferred to arbitrary degree structures or weaker background theories without an argument.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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Publication dates and editorial changes.