# Miguel Angel Mota: Forcing consequences of PFA together with the continuum large

Friday, July 27 at 1:30pm
Fields institute, Room 210

Speaker: Miguel Angel Mota (Fields)

Title: Forcing consequences of PFA together with the continuum large

Abstract: 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 $\mho$ does not follow from this arithmetical assumption. This is joint work with D. Asperó.

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