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    In M', the sentence θ_CH has no model. — Carmelics
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    Supports→The property of a second-order sentence having a model is not absolute relative to ZFC.

    In M', the sentence θ_CH has no model.

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    Absoluteness requires that the truth of a property be invariant across all model...In M, the sentence θ_CH has a model.M and M' are both countable transitive models satisfying a finite subset of ZFC.The property of a second-order sentence having a model is not absolute relative ...

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    In M', the same sentence θ_CH has no models, meaning M' does not model...94%In M, the sentence θ_CH has a model.92%In M, the sentence θ_CH has a model A, meaning M models 'A models θ_CH...89%There exists a sentence θ_¬CH of the empty vocabulary that has a model...82%

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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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