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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that The restriction to finite model theory means SO-exists captures NP only under a non-standard semantics that smuggles in finiteness as a hidden assumption.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Finiteness isn't 'hidden'—it's an explicit parameter of finite model theory as a stated mathematical framework, not a smuggled assumption.
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    • 2.The NP-SO correspondence is a meaningful mathematical result *within* finite model theory; results needn't apply universally to be valuable.
      ?

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    • 3.All practical computation involves finite structures; restricting semantics to finite models aligns theory with the problems it claims to address.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Second-order logic without finiteness restriction can express properties (like well-foundedness) unprovable in any recursively enumerable system.
      ?

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    • 2.NP-completeness is defined only for finite inputs; extending SO to infinite models changes the problem class fundamentally.
      ?

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    • 3.Standard semantics for SO allows quantification over all subsets; finite model theory artificially restricts this to make results tractable.
      ?

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