Possible behaviours of the reflection ordering of stationary sets

Journal of Symbolic Logic 60 (2):534-547 (1995)

Abstract
If S, T are stationary subsets of a regular uncountable cardinal κ, we say that S reflects fully in $T, S , if for almost all α ∈ T (except a nonstationary set) S ∩ α is stationary in α. This relation is known to be a well-founded partial ordering. We say that a given poset P is realized by the reflection ordering if there is a maximal antichain $\langle X_p; p \in P\rangle$ of stationary subsets of $\operatorname{Reg}(\kappa)$ so that $\forall p, q \in P \forall S \subseteq X_p, T \subseteq X_q \text{stationary}: (S We prove that if $V = L\lbrack\overset{\rightarrow\mathscr{U}}\rbrack, o^\mathscr{U} (\kappa) = \kappa^{++}$ , and P is an arbitrary well-founded poset of cardinality ≤ κ + then there is a generic extension where P is realized by the reflection ordering on κ
Keywords Stationary sets   reflection   measurable cardinals   repeat points
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DOI 10.2307/2275849
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[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Multiple Forcing.T. Jech - 1989 - Journal of Symbolic Logic 54 (3):1112-1113.
Sets Constructed From Sequences of Measures: Revisited.William J. Mitchell - 1983 - Journal of Symbolic Logic 48 (3):600-609.
Full Reflection of Stationary Sets Below ℵω.Thomas Jech & Saharon Shelah - 1990 - Journal of Symbolic Logic 55 (2):822 - 830.
Full Reflection at a Measurable Cardinal.Thomas Jech & Jiří Witzany - 1994 - Journal of Symbolic Logic 59 (2):615-630.

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