Subcompletions of representable relation algebras

TL;DR

This paper investigates the structure of certain non-representable relation algebras by embedding them into completions of representable algebras, revealing new insights into their subalgebra properties.

Contribution

It introduces a method to embed non-representable relation algebras into completions of representable ones, especially for Monk algebras, highlighting their subalgebra finiteness.

Findings

Many finite non-representable relation algebras embed into completions of representable algebras.

Finitely-generated subalgebras of these completions are finite.

The approach applies to almost all Monk algebras.

Abstract

Many finite symmetric integral non-representable relation algebras, including almost all Monk algebras, can be embedded in the completion of an atomic symmetric integral representable relation algebra whose finitely-generated subalgebras are finite.