Let \(S\) and \(T\) be stationary subsets of a regular cardinal \(\kappa\). \(S\) reflects fully in \(T\), \(S < T\), if for almost all \(\alpha\) in \(T\) (except for a nonstationary set), \(S \cap \alpha\) is stationary in \(\alpha\). This is the reflection ordering of stationary sets. It is known that this partial ordering is well-founded. A partial ordering \(P\) is realized by reflection ordering if there is a maximal antichain \(\langle X_p : p \in P \rangle\) of stationary subsets of \(\text{Reg} (\kappa)\) (the set of regular cardinals \(< \kappa)\) such that \(p < q\) iff for all stationary sets \(S \subseteq X_p\), \(T \subseteq X_q\), we have \(S < T\).
Here the author generalizes a construction of a joint paper with T. Jech [J. Symb. Logic 59, No. 2, 615-630 (1994; Zbl 0799.03060)]. Starting with a model \(V\) with some suitable properties he shows that for each well-founded partial ordering \(P\) with \(|P |\leq \kappa^+\) there is a generic extension where \(P\) is realized by the reflection ordering.