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Stationary reflection principles and two cardinal tree properties

Part of: Set theory

Published online by Cambridge University Press:  01 November 2013

Hiroshi Sakai
Affiliation:
Department of Computer Science and Systems Engineering Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, Japan ([email protected])
Boban Veličković
Affiliation:
Institut de Mathematiques de Jussieu - Paris Rive Gauche, Université Paris Diderot, 75205 Paris Cedex 13, France ([email protected])

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
Copyright
©Cambridge University Press 2013 

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