# Can nominalist logicians reject universals but accept universal statements?

I am aware that Nominalism comes in at least two flavors, one in particular is the denial of universals. Under this paradigm of Nominalsim, is it possible for a mathematician or even a logician to be a Nominalist? Can s/he outright deny universals while simultaneously accepting that given a universe U containing all objects under consideration, the proposition ∀x in U : p(x) is true for some propositional function p? If so, is it due to the individual merely carrying out the logical consequences of a given statement, while withholding belief concerning its truth with regard to reality broadly construed (e.g. physical reality, mathematical reality, etc)?