A representation theorem for measurable relation algebras with cyclic groups

Andréka, Hajnal and Givant, Steven (2019) A representation theorem for measurable relation algebras with cyclic groups. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 371. pp. 7175-7198. ISSN 0002-9947

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Abstract

A relation algebra is measurable if the identity element is a sum of atoms, and the square $ x;1;x$ of each subidentity atom $ x$ is a sum of non-zero functional elements. These functional elements form a group $ G_x$. We prove that a measurable relation algebra in which the groups $ G_x$ are all finite and cyclic is completely representable. A structural description of these algebras is also given.

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