2018/02/27 by Mohammadpour, Rahman, Velickovic, Boban · 2 citations
#03E05 #03E35 #03E55 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1802.10125
Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call \rm GM+(ω3,ω1) holds. This principle implies \rm ISP(ω2) and \rm ISP(ω3), and hence the tree property at ω2 and ω3, the Singular Cardinal Hypothesis, and the failure of the weak square principle \square(ω2,λ), for all regular λ≥ ω2. In addition, it implies that the restriction of the approachability ideal I[ω2] to the set of ordinals of cofinality ω1 is the non stationary ideal on this set. The consistency of this last statement was previously shown by Mitchell.