 If one is interested in simply the existence of some kind of model of the \(\lambda\)-calculus—one whose domain not necessarily consist of functions—one can find them by various well-known ‘syntactic’ constructions involving the theory \(\lambda\), not unlike the well-known Henkin constructions . These so-called term models, though, are an unsatisfactory solution to the question of whether there are ‘mathematical’ models of the \(\lambda\)-calculus.