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Possible behaviours of the reflection ordering of stationary sets

Published online by Cambridge University Press:  12 March 2014

Jiří Witzany
Jiří Witzany*
Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90024-1555, E-mail: jwitzany@math.ucla.edu
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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 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 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.

Keywords

Primary 03E3503E55.Stationary setsreflectionmeasurable cardinalsrepeat points
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 2 , June 1995 , pp. 534 - 547
Copyright
Copyright © Association for Symbolic Logic 1995

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