Echeloned saturation and forcing axioms

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 ${\mathrm{\aleph }}_2$, there are no weakly Laver ideals over ${\mathrm{\aleph }}_1$. We also prove that under Baumgartner’s axiom there are no Laver ideals over ${\mathrm{\aleph }}_2$.