Abstract
We try to take a first step to a theory of the structural properties of ideals over $\mathscr P_{\kappa}\lambda$, that was studied in detail by Baumgartner, Taylor and Wagon [1] for $\kappa$;. In defining the basic notions, P-points, Q-points, and selective ideals, we put importance on the behavior of the function on $\mathscr P_{\kappa}\lambda$ to the bounded ideal and Rudin-Keisler ordering.
Several facts hold similarly as on $\kappa$;, for instance, the bounded ideal is a nowhere Q-point. However some differences exist such as the bounded ideal is isomorphic to another ideal. We state the sufficient condition for ideals to be Q-points and the weakly normal ideals selective.
Citation
Yoshihiro Abe. "Structural properties of ideals over $\mathscr P_{\kappa}\lambda$ I." Tsukuba J. Math. 39 (1) 83 - 95, July 2015. https://doi.org/10.21099/tkbjm/1438951818
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