Indestructible Guessing Models and the Continuum

2015/10/18 by Cox, Sean, Krueger, John · 1 citation
#03E05 #03E35 #03E40 #03E65 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1510.05297

Abstract

We introduce a stronger version of an ω₁-guessing model, which we call an indestructibly ω₁-guessing model. The principle IGMP states that there are stationarily many indestructibly ω₁-guessing models. This principle, which follows from PFA, captures many of the consequences of PFA, including the Suslin hypothesis and the singular cardinal hypothesis. We prove that IGMP is consistent with the continuum being arbitrarily large.

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