Is any finite class a set under ZFC theory? or are there conditions still required to ensure that? condition like having a mathematical definition in first-order logic for any element of the class.
I am trying to give a mathematical representation of a collection of organisms, and it would be quite nice if it is a set, so I could describe a topology on it (or is it possible to have a concept of topology without the axiomatic set concept?). The other possibility may be working on category theory.
Thank you very much for your help!