In a data structures course, we see trees, balanced trees, hash tables. These have an important thing in common: we can use them to keep a collection of elements (with operations add and remove) and test for an element in the data structure.
I want to use them to define a "overarching" abstract data type, with each of them as an implementation. Is there a name for this ADT?
The set ADT unfortunately supports more operations (see https://en.wikipedia.org/wiki/Set_(abstract_data_type)#Operations)