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Semistationary and stationary reflection

Published online by Cambridge University Press:  12 March 2014

Hiroshi Sakai
Hiroshi Sakai*
Affiliation:
Graduate School of Information Science, Nagoya University, Japan, E-mail: sakai@rum.math.human.nagoya-u.ac.jp
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Abstract

We study the relationship between the semistationary reflection principle and stationary reflection principles. We show that for all regular cardinals λ ≥ ω2 the semistationary reflection principle in the space [λ]ω implies that every stationary subset of ≔ {α ∈ λ ∣ cf(α) = ω} reflects. We also show that for all cardinals λ ≥ ω3 the semistationary reflection principle in [λ]ω does not imply the stationary reflection principle in [λ]ω.

Keywords

Semistationary reflectionStationary reflection
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 1 , March 2008 , pp. 181 - 192
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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