I am a logician prior to any other designation and, frankly, see no validity in any further denomination. All that does is attempt to constrain and/or ignore logic by embracing terms and labels that seek to circumvent logic, something that cannot be done.
Interestingly it was a statement about your Realist position as stated on the Nominalist link the points up the error of Realism:
The realist answer is that all the green things are green in virtue of the existence of a universal; a single abstract thing
A single abstract thing is a contradiction in terms. If it is an abstract it is not a thing.
This commits the fallacy of Reification. In the hierarchy of conceptual development an abstract subsumes a number of concrete classes in a term that represents the classes of those objects but has no actual existence. The easiest example of this is if I say to you: "Hand me a furniture." The statement is logically absurd because furniture is an abstract representing several classes of concretes: lamps, chairs, coffee tables, sofas, desks in near endless profusion. Not only is there no abstract thing that represents furniture , there cannot be since the concept represents no thing. There can be no universal abstract outside of space time representing furniture because there is no such thing.
One has only to ask where the abstract concept for "starship" was before science fiction, (another abstract.)
The point here is philosophical Realism is logically fallacious. Which is why Aristotle came after Plato, not the other way around. Aristotle was smarter than Plato and had a clearer picture to the truth of things.
The subject of universals - Plato's forms - is well underway on another thread and I cannot see arguing the same points here. But I welcome you to the ongoing discussion, starting somewhere in the mid 200's on The Future of Biology thread. It is now in the mid 600's.