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Meaningless Sets in Infinitary Combinatory Logic Severi, Paula de Vries, Fer-Jan Infinitary Rewriting Combinatory Logic Meaningless Sets Confluence Normalisation In this paper we study meaningless sets in infinitary combinatory logic. So far only a handful of meaningless sets were known. We show that there are uncountably many meaningless sets. As an application to the semantics of finite combinatory logics, we show that there exist uncountably many combinatory algebras that are not a lambda algebra. We also study ways of weakening the axioms of meaningless sets to get, not only sufficient, but also necessary conditions for having confluence and normalisation. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Paula Severi and Fer-Jan de Vries 2012 Is Part Of LIPIcs, Volume 15, 23rd International Conference on Rewriting Techniques and Applications (RTA'12) (2012) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.RTA.2012.288 urn:nbn:de:0030-drops-34993 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2012.288 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode