 Now \(\theta_{\textrm{CH}}\), which is a sentence of the empty vocabulary, has a model if and only if the Continuum Hypothesis CH holds. Similarly, there is a sentence \(\theta_{\neg \textrm{CH}}\), which has a model if and only if the Continuum Hypothesis CH does not hold. This shows that the dependence of the semantics of second-order logic on the metatheoretic set theory is so deep that even questions that ZFC cannot solve can determine the truth or falsity of a sentence in a model.