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

David Aspero, Miguel Angel Mota

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

## Abstract

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.
Original language English 284–308 Annals of Pure and Applied Logic 167 3 21 Dec 2015 https://doi.org/10.1016/j.apal.2015.12.003 Published - Mar 2016

## Keywords

• Iterated forcing
• Club-guessing principles
• Side conditions
• Polychromatic Ramsey theory