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Ideals and combinatorial principles

Published online by Cambridge University Press:  12 March 2014

Douglas Burke  and
Yo Matsubara
Douglas Burke
Affiliation:
Department of Mathematical Science, University of Nevada, Las Vegas, Nevada 89154-4020, USA, E-mail: [email protected]
Yo Matsubara
Affiliation:
School of Informatics and Sciences, Nagoya University, Nagoya, 461-01Japan, E-mail: [email protected]
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Extract

It is well known that if σ is a strongly compact cardinal and λ a regular cardinal ≥ σ, then for every stationary subset X of {α < λ: cof (α) = ω} there is some β < λ such that X ⋂ β is stationary in β. In fact the existence of a uniform, countably complete ultrafilter over λ is sufficient to prove the same conclusion about stationary subsets of {α < λ: cof (α) = ω}. See [13] or [10]. By analyzing the proof of this theorem as presented in [10], we realized the same conclusion will follow from the existence of a certain ideal, not necessarily prime, on . Throughout we will assume that σ is a regular uncountable cardinal and use the word “ideal” to mean fine ideal.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 1 , March 1997 , pp. 117 - 122
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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