A Note on Absolutely Unorderable Combinatory Algebras.

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Title: A Note on Absolutely Unorderable Combinatory Algebras.
Authors: Lusin, Stefania1 slusin@dsi.unive.it, Salibra, Antonino1 salibra@dsi.unive.it
Source: Journal of Logic & Computation. Aug2003, Vol. 13 Issue 4, p481-502. 22p.
Subjects: Combinatory logic, Algebra, Axioms, Lambda calculus, Function algebras, Mathematical analysis
Abstract: 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. [ABSTRACT FROM PUBLISHER]
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Description
Abstract: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. [ABSTRACT FROM PUBLISHER]
ISSN:0955792X
DOI:10.1093/logcom/13.4.481