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Stationary reflection principles and two cardinal tree properties
Published online by Cambridge University Press: 01 November 2013
Abstract
We study the consequences of stationary and semi-stationary set reflection. We show that the semi-stationary reflection principle implies the Singular Cardinal Hypothesis, the failure of the weak square principle, etc. We also consider two cardinal tree properties introduced recently by Weiss, and prove that they follow from stationary and semi-stationary set reflection augmented with a weak form of Martin’s Axiom. We also show that there are some differences between the two reflection principles, which suggests that stationary set reflection is analogous to supercompactness, whereas semi-stationary set reflection is analogous to strong compactness.
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 14 , Issue 1 , January 2015 , pp. 69 - 85
- Copyright
- ©Cambridge University Press 2013
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