Minimal lambdatheories by ultraproducts
Abstract
A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambdatheory lambdabeta or the least sensible lambdatheory H (generated by equating all the unsolvable terms). A related question is whether, given a class of lambda models, there is a minimal lambdatheory 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 imodels. The method then applies also to graph models, Krivine models, coherent models and filter models. In particular, we build an imodel whose theory is the set of equations satisfied in all imodels.
 Publication:

arXiv eprints
 Pub Date:
 March 2013
 arXiv:
 arXiv:1303.7329
 Bibcode:
 2013arXiv1303.7329B
 Keywords:

 Computer Science  Logic in Computer Science;
 F.4.1;
 F.3.2
 EPrint:
 In Proceedings LSFA 2012, arXiv:1303.7136