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    The Immerman-Vardi theorem assumes linear orders on struc... — Carmelics
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    Challenges→P ≠ NP if and only if there exists a class of ordered structures definable in existential second-order logic which is not definable by a formula of FO(LFP)

    The Immerman-Vardi theorem assumes linear orders on structures, but natural computational problems lack canonical orderings.

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    1 reason for
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    Reasons For

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    Reason for
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    • 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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    Reasons Against

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    Reason against
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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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    Related

    All finite structures can be effectively ordered without loss of generality; the...Canonical orderings (lexicographic on finite domains) exist constructively; the ...Linear orders are mathematical conveniences, not claims about physical reality; ...Many natural problems (graph isomorphism, query evaluation) should be solvable w...
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    Order-dependent characterizations risk conflating logical expressiveness with ar...P ≠ NP if and only if there exists a class of ordered structures definable in ex...Real computational problems (databases, graphs, networks) have no inherent order...

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    2 (1 for, 1 against)
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