A representation theorem for measurable relation algebras with cyclic groups

Andréka, Hajnal; Givant, Steven

doi:10.1090/tran/7566

A representation theorem for measurable relation algebras with cyclic groups
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by Hajnal Andréka and Steven Givant PDF

Trans. Amer. Math. Soc. 371 (2019), 7175-7198 Request permission

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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