2026/07/18 by Hiroshi Sakai, M. Catalina Torres
#math.LO
The notion of n-stationary subsets of Pκλ for n < ω were introduced and studied by Cody, Lambie-Hanson & Zhang \citeCLHZ and Torres \citeT. They proved that if κ is supercompact, then Pκλ is n-stationary in itself for all cardinals λ≥ κ and all n < ω. In this paper we prove that strong compactness of κ does not imply the 2-stationarity of Pκλ for cardinals λ> κ. We also discuss Menas' Theorem for 1-stationary and 2-stationary subsets of Pκλ.