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    The biconditional conflates provability within a descript... — 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 that is not definable by any formula of FO(LFP).

    The biconditional conflates provability within a descriptive complexity framework with the truth of an independent computational conjecture, committing a use-mention error about mathematical equivalence.

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    Key Terms

    Biconditional(in formal logic)
    A logical statement that says two things are true if and only if each other is true; it's a two-way relationship (like saying 'you can vote if and only if you're 18').
    Computational conjecture(as used in computer science and mathematics)
    An educated guess about whether a particular computation or algorithm will work a certain way, that hasn't been proven yet.
    Descriptive complexity framework(as used in computer science and mathematical logic)
    A system for understanding how hard a problem is to solve or describe by looking at what logical tools you need to express it.
    Mathematical equivalence(as used in mathematics)
    When two different mathematical expressions or statements mean exactly the same thing and have the same value or truth.

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    Provability(as the standard by which large cardinal hypotheses are being compared)
    The ability to prove something is true using logical rules and established facts—whether a statement can be demonstrated with certainty.
    use-mention error(fundamental logic error in arguments)
    A logical mistake where you confuse using a word with talking about the word itself—like saying 'dog has three letters' when you meant the word 'dog' has three letters.

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    Modality & Possibility1 linkedPhilosophy of Language1 linked

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    P ≠ NP if and only if there exists a class of ordered structures definable in ex...

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