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Journal of Logic and Computation 2003 13(4):481-502; doi:10.1093/logcom/13.4.481
© 2003 by Oxford University Press
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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{at}dsi.unive.it, salibra{at}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.

Received 20 September 2001.


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