Can absoluteness just be an artifact of set theory?
I think most would agree that set theoretic constructions of some objects can be artificial. $\pi$ is a concept for us but the representation of $\pi$ as a set is pretty unnatural (no one would ask "does $x \in \pi$?"). On some level, this isn't really that big of a problem, whatever works works I guess.
But when it comes to absoluteness- absoluteness seems to specifically rely on the exact formulaic representation used to define the concept, and not necessarily anything to do with the concept by itself. So is it possible that we may have a concept that we intuitively expect to be absolute, but because of the strange/artificial set theoretic way we construct it, happen to be not absolute? Vice versa is it possible to have a concept we do not think should be absolute, but thanks to some set theoretic contortions we can express it in such a way that makes it absolute (even though that expression is pretty artificial and doesn't really convey the true idea of the concept, like using a set for $\pi$). Does that question make sense? Or is it too soft to be meaningful?