Translator Disclaimer
July, 2017 Some consequences from Proper Forcing Axiom together with large continuum and the negation of Martin's Axiom
Teruyuki YORIOKA
J. Math. Soc. Japan 69(3): 913-943 (July, 2017). DOI: 10.2969/jmsj/06930913

Abstract

Recently, David Asperó and Miguel Angel Mota discovered a new method of iterated forcing using models as side conditions. The side condition method with models was introduced by Stevo Todorčević in the 1980s. The Asperó–Mota iteration enables us to force some $\Pi_2$-statements over $H(\aleph_2)$ with the continuum greater than $\aleph_2$. In this article, by using the Asperó–Mota iteration, we prove that it is consistent that $\mho$ fails, there are no weak club guessing ladder systems, $\mathfrak{p}= {\mathrm{add}}(\mathcal{N}) = 2^{\aleph_0}>\aleph_2$ and ${MA}_{\aleph_1}$ fails.

Citation

Download Citation

Teruyuki YORIOKA. "Some consequences from Proper Forcing Axiom together with large continuum and the negation of Martin's Axiom." J. Math. Soc. Japan 69 (3) 913 - 943, July, 2017. https://doi.org/10.2969/jmsj/06930913

Information

Published: July, 2017
First available in Project Euclid: 12 July 2017

zbMATH: 06786984
MathSciNet: MR3685031
Digital Object Identifier: 10.2969/jmsj/06930913

Subjects:
Primary: 03E35
Secondary: 03E05, 03E17

Rights: Copyright © 2017 Mathematical Society of Japan

JOURNAL ARTICLE
31 PAGES


SHARE
Vol.69 • No. 3 • July, 2017
Back to Top