The independence of delta(1)(n)

In this paper we prove the independence of delta(n)(1) for n greater than o r equal to 3. We show that delta(4)(1) can be forced to be above any ordina l of L using set forcing. For delta(3)(1) we prove that it can he forced, u sing set forcing, to be above any L cardinal n such that kappa is Pi(1) def inable without parameters in L. We then show that delta(3)(1) cannot be for ced 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 car dinal.