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

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 \(I_\kappa | A = I_\kappa\).

MSC:

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