Indestructible guessing models and the continuum
Volume 239 / 2017
Fundamenta Mathematicae 239 (2017), 221-258
MSC: 03E05, 03E35, 03E40, 03E65.
DOI: 10.4064/fm340-1-2017
Published online: 26 May 2017
Abstract
We introduce a stronger version of an $\omega _1$-guessing model, which we call an indestructibly $\omega _1$-guessing model. The principle $\mathsf {IGMP}$ states that there are stationarily many indestructibly $\omega _1$-guessing models. This principle, which follows from $\mathsf {PFA}$, captures many of the consequences of $\mathsf {PFA}$, including the Suslin hypothesis and the singular cardinal hypothesis. We prove that $\mathsf {IGMP}$ is consistent with the continuum being arbitrarily large.
