Possible behaviours of the reflection ordering of stationary sets
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AbstractIf 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 α ∈ T (except a nonstationary set) S ∩ α 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: p ∈ P〉 of stationary subsets of Reg(κ) so thatWe 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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1968 ◽
Vol 9
(1)
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pp. 46-66
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2006 ◽
Vol 71
(3)
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pp. 1029-1043
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Keyword(s):
1995 ◽
Vol 118
(1)
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pp. 1-5
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1996 ◽
Vol 119
(2)
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pp. 287-295
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Keyword(s):