RADO'S CONJECTURE IMPLIES THAT ALL STATIONARY SET PRESERVING FORCINGS ARE SEMIPROPER

Abstract

Todorčević showed that Rado's Conjecture (RC) 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.