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

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 (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	16 May 2024 10:30
Last Modified:	01 Jul 2025 01:38
URI:	https://ueaeprints.uea.ac.uk/id/eprint/95229
DOI:	10.1142/S0219061324500211

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