Journal of the Mathematical Society of Japan

Reflection principles for $\omega_2$ and the semi-stationary reflection principle

Toshimichi USUBA

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Abstract

Starting from a model with a weakly compact cardinal, we construct a model in which the weak stationary reflection principle for $\omega_2$ holds but the Fodor-type reflection principle for $\omega_2$ fails. So the stationary reflection principle for $\omega_2$ fails in this model. We also construct a model in which the semi-stationary reflection principle holds but the Fodor-type reflection principle for $\omega_2$ fails.

Article information

Source
J. Math. Soc. Japan, Volume 68, Number 3 (2016), 1081-1098.

Dates
First available in Project Euclid: 19 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1468956160

Digital Object Identifier
doi:10.2969/jmsj/06831081

Mathematical Reviews number (MathSciNet)
MR3523539

Zentralblatt MATH identifier
06642405

Subjects
Primary: 03E35: Consistency and independence results
Secondary: 03E05: Other combinatorial set theory

Keywords
stationary reflection principle semi-stationary reflection principle Fodor-type reflection principle

Citation

USUBA, Toshimichi. Reflection principles for $\omega_2$ and the semi-stationary reflection principle. J. Math. Soc. Japan 68 (2016), no. 3, 1081--1098. doi:10.2969/jmsj/06831081. https://projecteuclid.org/euclid.jmsj/1468956160


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