There exist countable transitive models M and M' (subsets of ZFC) such that M satisfies the Continuum Hypothesis and M' does not.

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{“