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 |
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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: | |
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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