  A longstanding open problem in lambda calculus is whether there exist
continuous models of the untyped lambda calculus whose theory is exactly the
least lambda-theory lambda-beta or the least sensible lambda-theory H
(generated by equating all the unsolvable terms). A related question is
whether, given a class of lambda models, there is a minimal lambda-theory
represented by it. In this paper, we give a general tool to answer positively
to this question and we apply it to a wide class of webbed models: the
i-models. The method then applies also to graph models, Krivine models,
coherent models and filter models. In particular, we build an i-model whose
theory is the set of equations satisfied in all i-models.
