The independence of δn1

In this paper we prove the independence of delta(n)(1) for n greater than or equal to 3. We show that delta(4)(1) can be forced to be above any ordinal of L using set forcing. For delta(3)(1) we prove that it can he forced, using set forcing, to be above any L cardinal n such that kappa is Pi(1) definable without parameters in L. We then show that delta(3)(1) cannot be forced by a set forcing to be above every cardinal of L. Finally we present a class forcing construction to make delta(3)(1) greater than any given L cardinal.