A Note on Absolutely Unorderable Combinatory Algebras

S. Lusin
2003 Journal of Logic and Computation  
Plotkin [16] has conjectured that there exists an absolutely unorderable combinatory algebra, namely a combinatory algebra which cannot be embedded in another combinatory algebra admitting a non-trivial compatible partial order. In this paper we prove that a wide class of combinatory algebras admits extensions with a non-trivial compatible partial order.
doi:10.1093/logcom/13.4.481 fatcat:fn2nyncmcvdt7e3uue2xdic6gu