We also answer a question of Abraham and Cummings concerning the consistency of the failure of a certain polychromatic Ramsey statement together with the continuum large.
030">All these models are generic extensions via finite support iterations with symmetric systems of structures as side conditions, possibly enhanced with ω-sequences of predicates, and in which the iterands are taken from a relatively small class of forcing notions.
We also prove that the natural forcing for adding a large symmetric system of structures (the first member in all our iterations) adds ℵ1-many reals but preserves CH.