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On the equational consistency of order-theoretic models of the lambda-calculus Carraro, Alberto Salibra, Antonino Lambda calculus order-incompleteness partially ordered models Answering a question by Honsell and Plotkin, we show that there are two equations between lambda terms, the so-called subtractive equations, consistent with lambda calculus but not satisfied in any partially ordered model with bottom element. We also relate the subtractive equations to the open problem of the order-incompleteness of lambda calculus. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Alberto Carraro and Antonino Salibra 2012 Is Part Of LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2012.152 urn:nbn:de:0030-drops-36703 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.152 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode