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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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.

Item Type:	Article
Uncontrolled Keywords:	iterated forcing,club-guessing principles,side conditions,polychromatic ramsey theory
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Logic
Depositing User:	Pure Connector
Date Deposited:	07 Mar 2016 15:00
Last Modified:	24 Oct 2022 06:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/57378
DOI:	10.1016/j.apal.2015.12.003

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