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

David Aspero, Nutt Tananimit

Research output: Contribution to journalArticlepeer-review

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 $\MM_{\aleph_2}(\aleph_2\mbox{-c.c.})$.
Original languageEnglish
Number of pages31
JournalJournal of Mathematical Logic (jml)
Publication statusAccepted/In press - 16 May 2024

Cite this