# Separating club-guessing principles in the presence of fat forcing axioms

Aspero, David and Mota, Miguel Angel (2016) Separating club-guessing principles in the presence of fat forcing axioms. Annals of Pure and Applied Logic, 167 (3). 284–308. ISSN 0168-0072

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We separate various weak forms of Club Guessing at $$\omega_1$$ in the presence of $$2^{\aleph_0}$$ large, Martin's Axiom, and related forcing axioms. 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. All these models are generic extensions via finite support iterations with symmetric systems of structures as side conditions, possibly enhanced with $$\omega$$-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 $$\aleph_1$$-many reals but preserves CH.