Cofinality of normal ideals on P_kappa(λ), I

Given an ordinal delta <= lambda and a cardinal theta <= kappa, an ideal J on P_kappa(lambda) is said to be [delta]^{<theta}-normal if given B_e in J for e in P_theta(delta), the set of all a in P_kappa(lambda) such that a in B_e for some e in P_{|a cap theta|}(a cap delta) lies in J. We give necessary and sufficient conditions for the existence of such ideals and we describe the least one and we compute its cofinality.