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    The restriction to finite model theory means SO-exists ca... — Carmelics
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    Challenges→NP is captured by the logic SO-exists (second-order existential logic)

    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.

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    1 reason for
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    Reasons For

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    Reason for
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    • 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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    Reasons Against

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    Reason against
    ?
    • 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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    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    All practical computation involves finite structures; restricting semantics to f...Finiteness isn't 'hidden'—it's an explicit parameter of finite model theory as a...NP is captured by the logic SO-exists (second-order existential logic)NP-completeness is defined only for finite inputs; extending SO to infinite mode...
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    Second-order logic without finiteness restriction can express properties (like w...Standard semantics for SO allows quantification over all subsets; finite model t...The NP-SO correspondence is a meaningful mathematical result *within* finite mod...

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