An irregular filter model

In this paper we introduce a new filter model, which is of a kind that has escaped investigation up to now: it is induced by an intersection type theory generated in a non-standard way, by a preorder which puts into relation an atom with an arrow type, without equating them. We study the domain-theoretic implications of this choice, that are not trivial: in order to describe this filter model a new category is introduced and a special purpose functor defined. The filter model is then characterized as the initial algebra of the functor.