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    Home/Original/inverse
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    Inverse View

    It is not the case that The Immerman-Vardi theorem assumes linear orders on structures, but natural computational problems lack canonical orderings.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Linear orders are mathematical conveniences, not claims about physical reality; theorems using them remain valid for unordered domains.
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    • 2.All finite structures can be effectively ordered without loss of generality; the theorem's results transfer to order-free formulations.
      ?

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    • 3.Canonical orderings (lexicographic on finite domains) exist constructively; the claim confuses practical unavailability with theoretical impossibility.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Real computational problems (databases, graphs, networks) have no inherent ordering; imposing one introduces artificial assumptions.
      ?

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    • 2.Order-dependent characterizations risk conflating logical expressiveness with arbitrary representational choices made during encoding.
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    • 3.Many natural problems (graph isomorphism, query evaluation) should be solvable without order; requiring it suggests theoretical incompleteness.
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