2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/31339We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation of an arbitrary simple easy term is any filter which can be described in an uniform way by a predicate. This allows us to prove the consistency of a well-know lambda theory: this consistency has interesting consequences on the algebraic structure of the lattice of lambda theories.Logic in Computer ScienceF.3.2text