Rado's Conjecture implies that all stationary set preserving forcings are semiproper

Journal of Mathematical Logic 13 (1):1350001 (2013)
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Abstract

Todorčević showed that Rado's Conjecture implies CC*, a strengthening of Chang's Conjecture. We generalize this by showing that also CC**, a global version of CC*, follows from RC. As a corollary we obtain that RC implies Semistationary Reflection and, i.e. the statement that all forcings that preserve the stationarity of subsets of ω1 are semiproper.

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10.1142/s0219061313500013

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Citations of this work

Combinatorial dichotomies in set theory.Stevo Todorcevic - 2011 - Bulletin of Symbolic Logic 17 (1):1-72.
Rado’s Conjecture and its Baire version.Jing Zhang - 2019 - Journal of Mathematical Logic 20 (1):1950015.

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References found in this work

PFA Implies ADL(R).John Steel - 2005 - Journal of Symbolic Logic 70 (4):1255 - 1296.
Semistationary and stationary reflection.Hiroshi Sakai - 2008 - Journal of Symbolic Logic 73 (1):181-192.

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