Similarly to the epistemological problem, the problem of the application of mathematics is partially solved by the mathematical fictionalist. Field provides an account of the application of mathematics that does not require the truth of mathematical theories. As we saw, this demands that mathematics be conservative in the relevant sense. However, it is unclear whether Field has established the conservativeness of mathematics, given his restrictive way of introducing non-set-theoretic vocabulary into the axioms of set theory as part of his attempted proof of the conservativeness of set theory (Azzouni 2009b, p. 169, note 47; additional difficulties for the mathematical fictionalist program can be found in Melia 1998, 2000). Field was working with restricted ZFU, Zermelo-Fraenkel set theory with the axiom of choice modified to allow for Urelemente, objects that are not sets, but not allowing for any non-set-theoretic vocabulary to appear in the comprehension axioms, that is, replacement or separation (Field 1980, p. 17). This is, however, a huge restriction, given that when mathematics is actually applied, non-set-theoretic vocabulary, when translated into set-theoretic language, will have to appear in the comprehension axioms. As formulated by Field, the proof failed to address the crucial case of actual applications of mathematics.