## Mariangiola Dezani-Ciancaglini, Silvia Ghilezan, and Silvia Likavec.
Behavioural inverse limit lambda-models.
*Electronic Notes in Theoretical Computer Science*, 2004.
To appear.

We construct two inverse limit lambda-models which
completely characterise sets of terms with similar
computational behaviours: the sets of normalising, head
normalising, weak head normalising lambda-terms, those
corresponding to the persistent versions of these
notions, and the sets of closable, closable
normalising, and closable head normalising
lambda-terms. More precisely, for each 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.
We use the finitary logical description of the models,
obtained by defining suitable intersection type
assignment systems, to prove this.

Keywords: Lambda calculus, intersection types, models of lambda
calculus, Stone dualities, reducibility method

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