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

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Asperó, 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

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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
Uncontrolled Keywords:	weak square,forcing axiom failures,generalizations of martin’s axiom,weak chang’s conjecture,ℵ1.5-c.c. with respect to families of models with additional properties,logic ,/dk/atira/pure/subjectarea/asjc/2600/2609
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	16 May 2024 10:30
Last Modified:	23 Jul 2024 08:32
URI:	https://ueaeprints.uea.ac.uk/id/eprint/95229
DOI:	10.1142/S0219061324500211

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