A generalization of Martin's Axiom

David Aspero, Miguel Angel Mota

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
11 Downloads (Pure)

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 club-guessing 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 languageEnglish
Pages (from-to)193-231
Number of pages39
JournalIsrael Journal of Mathematics
Volume210
Issue number1
DOIs
Publication statusPublished - Sep 2015

Cite this