You may look at the paper Regressive functions and stationary sets by KirstenKarsten Steffens (In: Müller G.H., Scott D.S. (eds) Higher Set Theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1977), pp. 423–435. Lecture Notes in Mathematics 669 (1978)):
Review from Mathscinet:
The notions of closed unbounded sets, regressive functions, stationary sets and diagonal intersections are generalized to a wide range of partially ordered sets. The main theme is a generalization of Fodor's theorem and conditions are given under which the generalized theorem holds.