Nowhere precipitousness of the non-stationary ideal over P_kappa(lambda)

2001/02/06 by Yo Matsubara, Saharon Shelah, Matsubara, Yo +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO

paper · pdf · doi:10.48550/arxiv.math/0102045

published as J. Math. Log. 2 No. 1 (2002) 81--89

arxiv created 2001/02/06 · openalex publication_date 2001/02/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if lambda is a strong limit singular cardinal and kappa a regular uncountable cardinal < lambda, then NS_{kappa lambda}, the non-stationary ideal over P_kappa lambda, is nowhere precipitous. We also show that under the same hypothesis every stationary subset of P_kappa lambda can be partitioned into lambda^{< kappa} disjoint stationary sets.

Related

• The nonstationary ideal on P_κ(lambda) for lambda singular
• Some results on nonstationry ideal 2
• Nonreflecting stationary sets in P_kappa(lambda)
• PFA and precipitousness of the nonstationary ideal
• Cardinal characteristics on κ modulo non-stationary