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OUP > Journals > Computing/Engineer. & Mathematics/Stats. > Journal of Logic and Computation

Journal of Logic and Computation

Volume 13, Issue 4, June 2003: pp. 481-502

Original Article
A Note on Absolutely Unorderable Combinatory Algebras

Stefania Lusin and Antonino Salibra


Dipartimento di Informatica, Università Ca'Foscari di Venezia, Via Torino 155, 30172 Venezia, Italy. E-mail: slusin@dsi.unive.it, salibra@dsi.unive.it

Plotkin has conjectured that there exists an absolutely unorderable combinatory algebra, namely a combinatory algebra which cannot be embedded in another combinatory algebra admitting a nontrivial compatible partial order. In this paper we prove that a wide class of combinatory algebras admits extensions with a nontrivial compatible partial order.

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