Submission date: 29 January 2023

Abstract:

The theory of two binary relations has the strong amalgamation property when the first relation is assumed to be coarser than the second relation, and each relation satisfies a chosen set of properties from the following list: transitivity, reflexivity, symmetry, antireflexivity and antisymmetry. The amalgamation property is maintained when we add families of unary operations preserving all the relations. As a consequence, we get the existence of Fraï ssé limits for classes of finite structures.
The results fail, for general comparability conditions, when three or more binary relations are taken into account, or when we add an operation preserving just one relation.

Mathematics Subject Classification: 03C52, 06A75

Keywords and phrases:

Full text arXiv 2301.12482: pdf, ps.