Consistent and inconsistent generalizations of Martin's Axiom, weak square, and weak Chang's Conjecture

Aspero, David and Tananimit, Nutt (2024) Consistent and inconsistent generalizations of Martin's Axiom, weak square, and weak Chang's Conjecture. Journal of Mathematical Logic (jml). ISSN 0219-0613 (In Press)

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Abstract

We prove that the forcing axiom $\MA^{1.5}_{\aleph_2}(\mbox{stratified})$ implies $\Box_{\omega_1, \omega_1}$. Using this implication, we show that the forcing axiom $\MM_{\aleph_2}(\aleph_2\mbox{-c.c.})$ is inconsistent. We also derive weak Chang's Conjecture from $\MA^{1.5}_{\aleph_2}(\mbox{stratified})$ and use this second implication to give another proof of the inconsistency of $\MM_{\aleph_2}(\aleph_2\mbox{-c.c.})$.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Logic
Depositing User: LivePure Connector
Date Deposited: 16 May 2024 10:30
Last Modified: 16 May 2024 10:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/95229
DOI:

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