Reducts of relation algebras: The aspects of axiomatisability and finite representability
arXiv:2108.11692 · doi:10.1007/978-3-030-93100-1_17
Abstract
In this paper, we show that the class of representable residuated semigroups has the finite representation property. That is, every finite representable residuated semigroup is representable over a finite base. This result gives a positive solution to Problem 19.17 from the monograph by Hirsch and Hodkinson \cite{hirsch2002relation}. We also show that the class of representable join semilattice-ordered semigroups is pseudo-universal and it has a recursively enumerable axiomatisation. For this purpose, we introduce representability games for join semilattice-ordered semigroups.
arXiv admin note: text overlap with arXiv:2007.13079