A Note on Absolutely Unorderable Combinatory Algebras
S. Lusin · Journal of Logic and Computation · 2003
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.