User blog comment:Ytosk/Trying to define Bowers' K(n) systems/@comment-43798125-20191031221625/@comment-35470197-20191031223704

Of course, there are many other related issue. For example, since the OP does not declare what "axiomatic system" means, it can be a first order theory or something unspecified. As I wrote in my comment below, then such an abstract system does not define a natural number, because we have no fixed embedding of arithmetic.