Minimal lambda-theories by ultraproducts
type: Dataset
description: A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the $\lambda\beta$ or the least sensible lambda-theory $\cH$ (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.
issued: 2026-05-15T15:01:07.986884
language: en
modified: 2026-05-15T15:01:07.986890
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticspreprint
keyword: infoinfo-locomputer-science-cslogic-in-computer-science-cslo
keyword: preprints-working-papers-
landing page: https://hal.science/hal-00710340

Minimal lambda-theories by ultraproducts
type: Distribution
format: HTML
issued: 2026-05-15T15:01:07.990643
modified: 2026-05-15T15:01:07.975509
access URL: https://hal.science/hal-00710340

test_moissonnage_selune
type: Agent