 In 1963b, “Semantical Considerations on Modal Logic”, Kripke introduces a new generalization to the models of quantified modal systems. In 1959 a model was defined in a domain \(D\). As a result all worlds in one model had the same cardinality. In 1963b models are not given in a domain, hence worlds in the same model can be assigned different domains by a function \(\Psi\) that assigns domains to the elements \(H\) of \(K\). Given the variability of domains across worlds, Kripke can now construct counter-examples both to the Barcan Formula 