Minimal lambda-theories by ultraproducts

Antonio Bucciarelli
(PPS, Université Paris Diderot)
Alberto Carraro
(PPS, Université Paris Diderot)
Antonino Salibra
(DAIS, Università Ca' Foscari Venezia)

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.

In Delia Kesner and Petrucio Viana: Proceedings Seventh Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2012), Rio de Janeiro, Brazil, September 29-30, 2012, Electronic Proceedings in Theoretical Computer Science 113, pp. 61–76.
Published: 28th March 2013.

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