Structural properties of ideals over \(\mathcal{P}_\kappa\lambda\). I. (English) Zbl 1337.03069

Abe, Yoshihiro

Tsukuba J. Math. 39, No. 1, 83-95 (2015).

The author studies \(P_\kappa (\lambda)\) analogs of well-known properties of ideals on \(\kappa\) such as (weak) P-pointness, (weak) Q-pointness or (weak) selectivity and compares the properties of the noncofinal ideal \(I_{\kappa, \lambda}\) on \(P_\kappa (\lambda)\) with those of the noncofinal ideal \(I_\kappa\) on \(\kappa\). For example, it is shown that \(I_{\kappa, \lambda}\) is isomorphic to each one of its proper restrictions \(I_{\kappa, \lambda} | A\), whereas \(I_\kappa\) is isomorphic to \(I_\kappa | A\) just in case \(I_\kappa | A = I_\kappa\).

Reviewer: Pierre Matet (Caen)

MSC:

03E05	Other combinatorial set theory
03E35	Consistency and independence results
03E55	Large cardinals

Keywords:

\(P_\kappa (\lambda)\); bounded ideal; weak normality; structural property