Reflection principles for \(\omega_2\) and the semi-stationary reflection principle. (English) Zbl 1403.03103

Usuba, Toshimichi

J. Math. Soc. Japan 68, No. 3, 1081-1098 (2016).

Summary: 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.

MSC:

03E35	Consistency and independence results
03E05	Other combinatorial set theory
03E55	Large cardinals

Keywords:

stationary reflection principle; semi-stationary reflection principle; Fodor-type reflection principle