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    Post's problem demonstrates that intermediate c.e. Turing... — Carmelics
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    Challenges→K is Turing complete among the computably enumerable sets

    Post's problem demonstrates that intermediate c.e. Turing degrees exist between 0 and 0', meaning T-completeness requires independent justification beyond m-completeness alone.

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    Reasons For

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    Reason for
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    • 1.Post's problem proved intermediate c.e. degrees exist, establishing that m-completeness and T-completeness are distinct properties with different logical structures.
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    • 2.T-completeness captures Turing-decidability implications while m-completeness only captures many-one reduction; these capture fundamentally different computational relationships.
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    • 3.If T-completeness reduced to m-completeness, all intermediate c.e. degrees would be impossible; their existence proves independent justification is mathematically necessary.
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    Reasons Against

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    Reason against
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    • 1.T-completeness for c.e. sets does reduce to m-completeness in practice; intermediate c.e. degrees don't demonstrate otherwise, only that hierarchy is finer-grained.
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    • 2.The claim conflates logical independence from empirical computational differences; intermediate degrees show complexity distinctions, not that T-completeness needs separate foundational justification.
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    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    If T-completeness reduced to m-completeness, all intermediate c.e. degrees would...K is Turing complete among the computably enumerable setsPost's problem proved intermediate c.e. degrees exist, establishing that m-compl...T-completeness captures Turing-decidability implications while m-completeness on...
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    T-completeness for c.e. sets does reduce to m-completeness in practice; intermed...The claim conflates logical independence from empirical computational difference...

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