What is the relationship called between two sets that are both members of all the same sets?

Asked Jul 11 '20 at 07:45

Active Jul 11 '20 at 10:15

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Is there terminology for the relationship $\forall C(C\in D\implies(A\in C \iff B \in C))$ between $A$ and $B$, for some $D$?

I'm looking for a single word, or something shorthand for what's written in the title.

I assume the answer may be quite obvious, but I'm blanking at the moment. If there isn't such terminology, for shame!

edited Jul 11 '20 at 10:15

Asaf Karagila

asked Jul 11 '20 at 07:45

Graviton

Possibly "$A$ and $B$ are not separated by $D$" or "$A$ and $B$ are not distinguished by $D$". Not sure if I would use these without explanation though. – tkf Jul 11 '20 at 08:54
I don't know any such terminology. I'd say "$D$-equal" or that the sets "agree on $D$". – Asaf Karagila Jul 11 '20 at 10:15
In view of Leibniz's concept of the identity of indiscernibles, one might abbreviate the proposition as "$A$ and $B$ are $D$-indiscernible", but I agree with the comment that this usage would have to be defined. – Calum Gilhooley Jul 11 '20 at 16:28

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