We develop a new method for building forcing iterations with symmetric
systems of structures as side conditions. Using our method we prove that the
forcing axiom for the class of all the small finitely proper posets is
compatible with a large continuum.Comment: 35 page

Asperó, David

Mota, Miguel Angel

English

arXiv

We develop a new method for building forcing iterations with symmetric systems of structures as side conditions. Using our method we prove that the forcing axiom for the class of all the finitely proper posets of small size is compatible with the continuum being larger than the second uncountable cardinal . In particular, this answers a question of Justin Moore by showing that ? does not follow from this arithmetical assumption

Forcing consequences of PFA together with the continuum large

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