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Oct 21 at 11:23 comment added YCor A variant using $A=P(\omega)/$fin is: for any $f\in \mathrm{Hom}(A,\mathbf{Z}/2\mathbf{Z})$, $R_f=\mathrm{Ker}(f)$. Topologically, this corresponds to: given the point $x$ determined by $f$ in $\beta^*\omega$ (Stone-Cech remainder), $R_f$ is the set of clopen subsets of $\beta^*\omega$ not containing $x$.
Oct 21 at 11:17 comment added YCor (Note that this example of $R$ is countable, and it can be shown to be the only one up to isomorphism.)
Oct 21 at 3:48 history answered YCor CC BY-SA 4.0