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

Item Type: | Article |
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Faculty \ School: | Faculty of Science > School of Mathematics |

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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