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    In M, the sentence θ_CH has a model A, meaning M models '... — Carmelics
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    Supports→The property of a model satisfying a second-order sentence is not absolute relative to ZFC.

    In M, the sentence θ_CH has a model A, meaning M models 'A models θ_CH'.

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    If a property were absolute relative to ZFC, its truth value would be the same a...In M', the same sentence θ_CH has no models, meaning M' does not model 'A models...The property of a model satisfying a second-order sentence is not absolute relat...

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    There exist countable transitive models M and M' (subsets of ZFC) such that M sa...

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    In M, the sentence θ_CH has a model.97%In M', the same sentence θ_CH has no models, meaning M' does not model...90%In M', the sentence θ_CH has no model.89%Whether 'N ⊨ θ' holds therefore depends on which model of ZF is taken ...84%

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    A more serious case of non-absoluteness is the sentence \(\theta_{\textrm{CH}}\) of §5.3. The sentence \(\theta_{\textrm{CH}}\) of the empty vocabulary has a model if and only if the Continuum Hypothesis is true. If \(T\subseteq \ZFC\) is finite, then there are countable transitive models \(M\subseteq M'\) such that one, say M, satisfies CH and the other, in this case \(M'\), does not (by Cohen 1966). In M the sentence \(\theta_{\textrm{CH}}\) has a model \(\ma\), that is, \(M\models \textrm{“

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