Rational separability over a global field

Let F be a finitely generated held and let j:F --> N be a weak presentation of F, i.e. an isomorphism from F onto a field whose universe is a subset of N and such that all the field operations are extendible to total recursive functions. Then if R(1) and R(2) are recursive subrings of F, for all weak presentations j of F,j (R(1)) is Turing reducible to j(R(2)) if and only if there exists a finite collection of non-constant rational functions {G(i)} over F such that for every x is an element of R(1) for some i, G(i)(x) is an element of R(2). We investigate under what circumstances such a collection of rational functions exists and conclude that in the case when R(1) not subset of or equal to R(2) are both holomorphy rings and F is of characteristic 0 or is an algebraic function field over a perfect field of constants, the existence of the above-described collection of rational functions is equivalent to the requirement that the non-archimedean primes which do not appear as poles of elements of R(2) do not have factors of relative degree 1 in some simple extension of K.