Equationally distinct countable simple {\textsf{Q}}-relation algebras (Q607448)

Tarski's Q-relation algebras are relation algebras with two elements that behave like projection functions. The author extracts a representation for countable simple Q-relation algebras from the proof in [\textit{R.\ Maddux}, ``Some sufficient conditions for the representability of relation algebras'', Algebra Univers. 8, 162--172 (1978; Zbl 0386.03033)] that all Q-relation algebras (and more) are representable. This representation preserves well-foundedness of binary relations when applied to proper Q-relation algebras (in which the elements are already relations) and provides a link between relation algebras and countable models of set theory. The author proves the existence of equationally distinct countable simple Q-relation algebras using, as an example, the sentence CH, which is known to be independent of ZFC.