Consistent and Inconsistent Generalizations of Martin's Axiom and Weak Square

Abstract: We prove that the forcing axiom $\textsf{MA}^{1.5}_{\aleph_2}(\text{stratified})$ implies $\square_{\omega_1, \omega_1}$. Using this implication, we show that the forcing axiom $\textsf{MM}_{\aleph_2}(\aleph_2\text{-c.c.})$ is inconsistent.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.