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It is not the case that Post's problem (1944) demonstrated that intermediate degrees exist between decidable and complete r.e. sets, undermining claims of a single highest degree.
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Reasons For
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Reason for
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1.
Post's theorem concerns only r.e. sets; intermediate degrees may not exist among all Turing degrees, limiting the scope of the general claim.
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2.
The claim conflates 'multiple degrees' with 'no highest degree'—there could still be maximal degrees even with intermediate ones present.
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3.
Post's work refutes a specific 1944-era conjecture but doesn't establish which degree-theoretic claims about undecidability were actually being defended.
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Reasons Against
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Reason against
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1.
Post's construction of intermediate degrees definitively proves the degree structure is non-linear, confirming genuine complexity gaps exist.
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2.
The existence of intermediate r.e. degrees demonstrates Turing reducibility creates a rich hierarchy, not a binary decidable/undecidable partition.
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3.
Post's result provides concrete mathematical evidence against oversimplified claims that undecidability represents a single 'top' difficulty level.
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