## 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 $\MM_{\aleph_2}(\aleph_2\mbox{-c.c.})$.

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 $\MM_{\aleph_2}(\aleph_2\mbox{-c.c.})$.

Original language | English |
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Article number | 2450021 |

Number of pages | 31 |

Journal | Journal of Mathematical Logic (jml) |

Early online date | Jul 2024 |

DOIs | |

Publication status | E-pub ahead of print - Jul 2024 |

## 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