Assume for the sake of this question that mathematics is reducible to set theory in such a way that the only mathematical objects there really are, are sets.
Suppose further that the Indispensability Argument is successful and shows us that we need to believe in sets.
My question is would this show us that impure set theory is indispensable? Does physics require impure sets? In other words, are there primitive relations of physics (where a primitive relation of physics is something unique to physics--- not something like equality/identity) that hold between mathematical entities (like numbers) and physical entities?
Are there any good papers that discuss indispensability and impure set theory?