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    Home/Original/inverse
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    Inverse View

    It is not the case that K is Turing complete among the computably enumerable sets

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Many-one completeness establishes K as a ceiling for m-reducibility, but Turing reducibility permits oracle queries that m-reductions structurally forbid.
      ?

      Think about whether this reason is strong or weak

    • 2.The inference from m-completeness to T-completeness conflates degree-theoretic hierarchy levels: m-degrees are strictly finer than T-degrees, so completeness in one does not automatically transfer upward.
      ?

      Think about whether this reason is strong or weak

    • 3.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.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Turing completeness among c.e. sets requires that K can simulate any c.e. set's membership problem, but this presupposes a fixed model of computation whose universality is not logically necessary.
      ?

      Think about whether this reason is strong or weak

    • 2.Kreisel and Sacks showed that relativized computability contexts admit c.e. sets whose Turing degree structure diverges from the unrelativized case, undermining the generality of K's completeness claim.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.K is many-one complete among the c.e. sets
      ?

      Think about whether this reason is strong or weak

    • 2.Many-one reducibility implies Turing reducibility
      ?

      Think about whether this reason is strong or weak

    • 3.Therefore any c.e. set is Turing reducible to K
      ?

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