TY - JOUR
T1 - ECHELONED SATURATION AND FORCING AXIOMS
AU - Garti, Shimon
N1 - Publisher Copyright:
© Royal Irish Academy.
PY - 2024
Y1 - 2024
N2 - We show that under the failure of Chang’s conjecture and the assumption that Mar-tin’s axiom holds and the continuum is above ω2, there are no weakly Laver ideals over ℵ1. 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 ℵ2. This statement generalises Larson’s result at ℵ1 under Martin’s axiom.
AB - We show that under the failure of Chang’s conjecture and the assumption that Mar-tin’s axiom holds and the continuum is above ω2, there are no weakly Laver ideals over ℵ1. 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 ℵ2. This statement generalises Larson’s result at ℵ1 under Martin’s axiom.
UR - http://www.scopus.com/inward/record.url?scp=85205347905&partnerID=8YFLogxK
U2 - 10.1353/mpr.2024.a919661
DO - 10.1353/mpr.2024.a919661
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AN - SCOPUS:85205347905
SN - 1393-7197
VL - 124A
SP - 1
EP - 14
JO - Mathematical Proceedings of the Royal Irish Academy
JF - Mathematical Proceedings of the Royal Irish Academy
IS - 1
ER -