 For the sake of a more comprehensive survey, we want to go even further.  As the next step, we will introduce two forms of structuralism that are closely related to relativist structuralism and concept structuralism but not identical with either. (Both are forms of “abstractionist structuralism”, as we will see.)  Let us start again with a higher-order concept defined by an axiom system, such as “natural number system”, together with the set-theoretic systems falling under it. However, instead of identifying the corresponding structure either with that concept or with some pragmatically chosen system falling under it, we focus on the whole equivalence class determined by the concept.