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On weakly stationary sets

Author: Qi Feng
Journal: Proc. Amer. Math. Soc. 105 (1989), 727-735
MSC: Primary 03E05; Secondary 03E35, 03E55
MathSciNet review: 946635
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Abstract: We consider whether every weakly stationary set is stationary. We show that if $ {0^\char93 }$ does not exist then every weakly stationary set is stationary. Also there is a weakly stationary nonstationary set on $ [\omega_2]^{\aleph_1}$ if and only if Chang's conjecture holds. From a $ \omega_1$-Erdös cardinal, we get a model in which $ 2^{{\aleph_0}} > \omega_2$ and all the subsets of $ 2^{\aleph_0}$ of order type $ \omega_1$ form a weakly stationary set which is nonstationary.

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Keywords: Weakly stationary, stationary
Article copyright: © Copyright 1989 American Mathematical Society