Two Behavioural Lambda Models

We build two inverse limit lambda models which characterize completely sets of terms having similar computational behaviour. More precisely for each one of these sets of terms there is a corresponding element in at least one of the two models such that a term belongs to the set if and only if its interpretation (in a suitable environment) is greater than or equal to that element. This is proved by using the finitary logical description of the models obtained by defining suitable intersection type assignment systems.