Abstract
We define the \(\aleph_{1.5}\)chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom; in fact, \(MA^{1.5}_{<\kappa}\) implies \(MA_{<\kappa}\). Also, \(MA^{1.5}_{<\kappa}\) implies
certain uniform failures of clubguessing on \(\omega_1\) that do not seem to have been considered in the literature before. We show, assuming CH and given any regular cardinal \(\kappa\geq\omega_2\) such that \(\mu^{\aleph_0}< \kappa\) for all \(\mu < \kappa\) and such that \(\diamondsuit(\{\alpha<\kappa\,:\, cf(\alpha)\geq\omega_1\})\) holds, that there is a proper \(\aleph_2\)c.c. partial order of size \(\kappa\) forcing \(2^{\aleph_0}=\kappa\) together with \(MA^{1.5}_{<\kappa}\).
certain uniform failures of clubguessing on \(\omega_1\) that do not seem to have been considered in the literature before. We show, assuming CH and given any regular cardinal \(\kappa\geq\omega_2\) such that \(\mu^{\aleph_0}< \kappa\) for all \(\mu < \kappa\) and such that \(\diamondsuit(\{\alpha<\kappa\,:\, cf(\alpha)\geq\omega_1\})\) holds, that there is a proper \(\aleph_2\)c.c. partial order of size \(\kappa\) forcing \(2^{\aleph_0}=\kappa\) together with \(MA^{1.5}_{<\kappa}\).
Original language  English 

Pages (fromto)  193231 
Number of pages  39 
Journal  Israel Journal of Mathematics 
Volume  210 
Issue number  1 
DOIs  
Publication status  Published  Sep 2015 
Profiles

David Aspero
 School of Engineering, Mathematics and Physics  Associate Professor in Pure Mathematics
 Logic  Member
Person: Research Group Member, Academic, Teaching & Research