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Possible behaviours of the reflection ordering of stationary sets

  • Jiří Witzany (a1)
Abstract

If S, T are stationary subsets of a regular uncountable cardinal κ, we say that S reflects fully in T, S < T, if for almost all αT (except a nonstationary set) Sα 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 〈Xp: pP〉 of stationary subsets of Reg(κ) so that

We prove that if , 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.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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