Echeloned Saturation and Forcing Axioms
Shimon Garti · Mathematical Proceedings of the Royal Irish Academy · 2024
Abstract: We show that under the failure of Chang’s conjecture and the assumption that Martin’s axiom holds and the continuum is above ω 2, there are no weakly Laver ideals over ℵ 1. This gives an answer to a question of Paul Larson’s. Likewise, we prove that under Baumgartner’s axiom there is no Laver ideal over ℵ 2. This statement generalises Larson’s result at ℵ 1 under Martin’s axiom.