You may look at the paper [Regressive functions and stationary sets](https://doi.org/10.1007/BFb0103112) by Karsten 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](https://mathscinet.ams.org/mathscinet-getitem?mr=520198):

>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.