Forcing consequences of 𝑃𝐹𝐴 together with the continuum large

Asperó, David; Mota, Miguel Angel

doi:10.1090/S0002-9947-2015-06205-9

Forcing consequences of $\mathsc {PFA}$ together with the continuum large
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by David Asperó and Miguel Angel Mota PDF

Trans. Amer. Math. Soc. 367 (2015), 6103-6129 Request permission

Abstract:

We develop a new method for building forcing iterations with symmetric systems of structures as side conditions. Using this method we prove that the forcing axiom for the class of all finitely proper posets of size $\aleph _1$ is compatible with $2^{\aleph _{0}}> \aleph _2$. In particular, this answers a question of Moore by showing that $\mho$ does not follow from this arithmetical assumption.

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