You make relations and functions out of sets and prove theorems about them, reducing definition of things in terms of belonging to a set. This isn't particularly complicated.
> The Peano axioms can be derived from set theoretic constructions of the natural numbers and axioms of set theory such as ZF.[15]
If you're going against the general consensus you should present something more than nebulous assertions that it's wrong.
> If you're going against the general consensus you should present something more than nebulous assertions that it's wrong.
burden of proof is on the one who claims something exists.