>>24640991
>Can one construct an infinite regress in mathematical terms?
Yes, it’s trivial.

>Would such a construction prove the possibility of infinite regress?
Depends on what you mean by “possible.” It shows that a human being can define a concept which entails an infinite regress, but it doesn’t prove that this concept maps to some fact about the empirical world.

>Would it have ramifications in the philosophy of mathematics?
Yes, but banal ones. Most contemporary philosophers of math are social constructivists (to whom any specific mathematical object is merely a thing someone made up) or neoplatonists (to whom infinities are attractive, because they show a gap between the world of mathematical forms and the material world).