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    Henkin semantics admits a completeness result for second-... — Carmelics
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    Supports→Second-order logic satisfies the Completeness Theorem when Henkin models are used, allowing semantic arguments to be turned into syntactic formal proofs

    Henkin semantics admits a completeness result for second-order logic

    Philosophy of LanguageTruth & Knowledge
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    Second-order logic satisfies the Completeness Theorem when Henkin models are use...The semantic argument must be valid in all Henkin models, not only in all full H...

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    Let \(c,d\in (a,b)\) such that \(f(c)<0\) and \(f(d)>0\). Without loss of generality, \(c<d\). Let \(X=\{e\in(a,b) : f(e)<0\}\). Since we have relation variables for subsets of the domain, we can think of X simply as a value of such a relation variable. , \(X=\{e : e\notin X\}\)) and then we should not be able to claim that it exists. However, in this case the Comprehension Axiom Schema implies that X exists. Clearly, \(X\ne\emptyset\) and X is bounded from above by d. One of the sec

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