 The cardinality argument shows that if we are to have a semantics for \(\lambda\)-calculus, the interpretation of \(\lambda\)-terms cannot simply be functions in the set-theoretic sense of the term. There are, however, interpretations of \(\lambda\)-calculus. The first model, \(D_{\infty}\), was found by D. Scott; other models were found later. These models solve the cardinality problem by restricting the domain \(X\) of interpretation, so that, in them, \(X\) is in a suitable sense isomorphic to the ‘function space’ \(X^X\).