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    Henkin's completeness theorem doesn't 'lose' categoricity... — Carmelics
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    Challenges→As Henkin (1950) demonstrated, weakening the semantics of second-order logic to general models preserves completeness but loses categoricity, so validity in full models and validity relative to θ come apart.

    Henkin's completeness theorem doesn't 'lose' categoricity—full second-order logic was never categorical for all theories, only for specific axiomatizations like PA.

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