%0 Journal Article
%T Minimal lambda-theories by ultraproducts
%A Antonio Bucciarelli
%A Alberto Carraro
%A Antonino Salibra
%J Electronic Proceedings in Theoretical Computer Science
%D 2013
%I Open Publishing Association
%R 10.4204/eptcs.113.8
%X 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.
%U http://arxiv.org/pdf/1303.7329v1