A generalization of Martin's Axiom

Aspero, David and Mota, Miguel Angel (2015) A generalization of Martin's Axiom. Israel Journal of Mathematics, 210 (1). pp. 193-231. ISSN 0021-2172

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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 \(MA^{1.5}_{<\kappa}\).

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Logic
Depositing User: Pure Connector
Date Deposited: 19 Dec 2015 07:04
Last Modified: 24 Oct 2022 06:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/55751
DOI: 10.1007/s11856-015-1250-0


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