 Recall the definition of the sentence \(\theta_{\textrm{EC}}(P,R)\) in  §5.3,  which says that the interpretations of the predicates P and R have the same cardinality. Cardinality is not an absolute property. Two sets (even two ordinals) can be of different cardinality in one transitive model of ZFC and of the same cardinality in a transitive extension. It is easy to see that “\(\mm\models_s\theta_{\textrm{EC}}(P,R)\)” is not absolute relative to ZFC. Essentially, the reason is that two sets have the same cardinality if there is a bijection between them. In a small transitive set it may happen that the sets are there but the bijection manifesting their equicardinality is not. The bijection may be one obtained by the method of forcing. Or the lack of the bijection may be the result of applying the Downward Löwenheim-Skolem  Theorem[6].