Generalizations of Martin's Axiom, weak square, weak Chang's Conjecture, and a forcing axiom failure

David Aspero, Nutt Tananimit

We prove that the forcing axiom $MA^{1.5}_{\aleph_2}(\mbox{stratified})$ implies ${\square }_{{\omega }_1,{\omega }_1}$. Using this implication, we show that the forcing axiom $MM_{\aleph_2}(\aleph_2\m…