Echeloned saturation and forcing axioms

Abstract

Addressing a question of Paul Larson we prove the following statement. If Chang's conjecture fails, Martin's axiom holds and the continuum is greater than ${\aleph }_2$, there are no weakly Laver ideals over ${\aleph }_1$. We also prove that under Baumgartner's axiom there are no Laver ideals over ${\aleph }_2$.