## 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:

 300000 Other combinatorial set theory 3e+35 Consistency and independence results 3e+55 Large cardinals
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