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Relation algebras, a kind of Boolean algebras with operators (BAOs), have been introduced by Alfred Tarski to provide an algebraisation of binary relations. In this survey, we discuss several results about them. In particular, we focus on the questions of representability.A representation of a relation algebra is an isomorphism of a given algebra with some algebra of binary relations (relation set algebra). The problem is that there exist non-representable algebras. That is, we do not have a representation theorem, unlike Boolean algebras or groups. In this talk, we introduce representability back-and-forth games for relation algebras. We figure out how one can characterise representable relation algebras using those games. Preview: Our website: VK: FB:
