Let $M$ be an arbitrary set and let $\mathscr{F}$ be a family of subsets of $M$. Is there a known name for the following equivalence relation or its corresponding partition?


$\sim\_{M,\mathscr{F}}\,=\bigl\{(x,y)\in M\times M\bigm|\forall A\in\mathscr{F}\,(x\in A\leftrightarrow y\in A)\bigr\}$.



Is there a name for this equivalence relation?
$\mathscr F$-indistinguishability.


In analogy with [Topological indistinguishability](https://en.m.wikipedia.org/wiki/Topological_indistinguishability).


