Possible Behaviours of the Reflection Ordering of Stationary Sets
Witzany, Jiri
J. Symbolic Logic, Tome 60 (1995) no. 1, p. 534-547 / Harvested from Project Euclid
If $S, T$ are stationary subsets of a regular uncountable cardinal $\kappa$, we say that $S$ reflects fully in $T, S < T$, if for almost all $\alpha \in T$ (except a nonstationary set) $S \cap \alpha$ is stationary in $\alpha$. 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 $\forall p, q \in P \forall S \subseteq X_p, T \subseteq X_q \text{stationary} : (S < T \leftrightarrow p < p q).$ 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 $\leq \kappa^+$ then there is a generic extension where $P$ is realized by the reflection ordering on $\kappa$.
Publié le : 1995-06-14
Classification:  Stationary sets,  reflection,  measurable cardinals,  repeat points,  03E35,  03E55
@article{1183744754,
     author = {Witzany, Jiri},
     title = {Possible Behaviours of the Reflection Ordering of Stationary Sets},
     journal = {J. Symbolic Logic},
     volume = {60},
     number = {1},
     year = {1995},
     pages = { 534-547},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183744754}
}
Witzany, Jiri. Possible Behaviours of the Reflection Ordering of Stationary Sets. J. Symbolic Logic, Tome 60 (1995) no. 1, pp.  534-547. http://gdmltest.u-ga.fr/item/1183744754/