Obviously the big question is whether it's wise to add these protocols. But I got curious and did a little research just on the naming question, to see if "intensional set" and "extensional set" are well-established mathematical terms for different kinds of sets. Seems like they're not.
I checked two reference works -- The Princeton Companion to Mathematics and the Encyclopedic Dictionary of Mathematics (2nd edition). I looked in their tables of contents, their indexes, and in their articles discussing set theory, and there is no mention of the idea of an "intentional set" or an "extensional set". Also, anecdotally, I did some math in grad school and never ran into the terms.
The terms "extensional" and "intensional" originate in philosophy of l