SUBCOMPLETIONS OF REPRESENTABLE RELATION ALGEBRAS
Roger D. Maddux · 2016
The variety of representable relation algebras is closed under canonical extensions but not closed under completions. What variety of relation algebras is generated by completions of representable relation algebras? Does it contain all relation algebras? It contains all representable finite relation algebras, and this paper shows that it contains many non-representable finite relation algebras as well. For example, every Monk algebra with six or more special elements (called “colors”) is a subalgebra of the completion of an atomic symmetric integral representable relation algebra whose finitely-generated subalgebras are finite.