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arXiv · 2108.11692

Reducts of relation algebras: The aspects of axiomatisability and finite representability

Daniel Rogozin
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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.

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Daniel Rogozin. 2021-08-26. Reducts of relation algebras: The aspects of axiomatisability and finite representability. https://doi.org/10.1007/978-3-030-93100-1_17

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