Subtraction is not closed over positive integers, which is untidy. The point of Tarski’s conjecture was to propose a minimal number of axioms and operations, AFAICS they define the standard semiring of positive integers (with the natural definition of exponentiation added).

(Edit: positive integers aren’t exactly a semiring because 0 is excluded, although some authors do define a semiring without the requirement of an additive identity element.)

Well, yes, but negative numbers are also well known to every high school math student.