> Moreover, Robinson arithmetic can be interpreted in general set theory, a small fragment of ZFC.
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t...
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t...
its hard to me to tell what this means formally(as I said I am not expert). There is no "interpret" operator in zfc. I believe what it says if you add some robinson axioms + some logical rules on top of zfc, you can carry your results.
You don't need to add any axioms, you just build some sets to represent numbers and make operations that act the same way as arithmetic, define some equality relations. Then you derive rules of arithmetic for your handcrafted arithmetic using ZF axioms and you're good. You get axioms of arithmetic derived from your regular axioms without adding them as new axioms to your theory.
which is already "just" some non trivial problem(there is no "operations" in set theory), and we are discussing if it is achievable.
> 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.