 In set-theoretic structuralism, and in relativist structuralism more broadly, the only mathematical objects at play are those that axiomatic set theory, possibly with urelements, allows us to introduce. We do not need to postulate abstract structures in addition. For that reason, the position is another form of eliminative structuralism (while it is not fully eliminative insofar as it countenances sets).  In fact, set-theoretic relational systems (the set-theoretic models of theories) are themselves taken to be the relevant structures here. (It is exactly such relational systems that are called “structures” in many mathematics textbooks.) However, there is another option in connection with the latter. Namely, we can also identify the structure of the natural numbers, say, with the (higher-order) concept defined by the Dedekind-Peano axioms; similarly for other (categorical) axiom systems. This leads to yet another eliminative form of structuralism: “concept structuralism” (cf. Isaacson 2010, Feferman 2014, also Ketland 2015, Other Internet Resources).